LMFDB - Complex character search results

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Results (1-50 of 57 matches)

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Label	Degree	Type	Faithful	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
11664.bf.1a	$1$	R		$1$	$\Q$	11664.bf.1a	$C_3^5:(C_2\times S_4)$	$C_1$	$1$	1.a1	$11664$	1.a1	$11664$	$1$	$1$
11664.bf.1b	$1$	R		$1$	$\Q$	11664.bf.1b	$C_3^5:(C_2\times S_4)$	$C_2$	$2$	2.c1	$5832$	1.a1	$11664$	$1$	$1$
11664.bf.1c	$1$	R		$1$	$\Q$	11664.bf.1c	$C_3^5:(C_2\times S_4)$	$C_2$	$2$	2.b1	$5832$	1.a1	$11664$	$1$	$1$
11664.bf.1d	$1$	R		$1$	$\Q$	11664.bf.1d	$C_3^5:(C_2\times S_4)$	$C_2$	$2$	2.a1	$5832$	1.a1	$11664$	$1$	$1$
11664.bf.2a	$2$	R		$1$	$\Q$	11664.bf.2a	$C_3^5:(C_2\times S_4)$	$S_3$	$6$	6.b1	$1944$	6.b1	$1944$	$6$	$1$
11664.bf.2b	$2$	R		$1$	$\Q$	11664.bf.2b	$C_3^5:(C_2\times S_4)$	$S_3$	$6$	6.a1	$1944$	6.a1	$1944$	$6$	$1$
11664.bf.2c	$2$	R		$1$	$\Q$	11664.bf.2c	$C_3^5:(C_2\times S_4)$	$D_6$	$12$	12.a1	$972$	6.a1	$1944$	$6$	$1$
11664.bf.2d	$2$	R		$1$	$\Q$	11664.bf.2d	$C_3^5:(C_2\times S_4)$	$D_6$	$12$	12.b1	$972$	6.b1	$1944$	$6$	$1$
11664.bf.3a	$3$	R		$1$	$\Q$	11664.bf.3a	$C_3^5:(C_2\times S_4)$	$S_4$	$24$	24.a1	$486$	24.a1	$486$	$24$	$1$
11664.bf.3b	$3$	R		$1$	$\Q$	11664.bf.3b	$C_3^5:(C_2\times S_4)$	$S_4$	$24$	24.a1	$486$	24.a1	$486$	$24$	$1$
11664.bf.3c	$3$	R		$1$	$\Q$	11664.bf.3c	$C_3^5:(C_2\times S_4)$	$C_2\times S_4$	$48$	48.a1	$243$	24.a1	$486$	$24$	$1$
11664.bf.3d	$3$	R		$1$	$\Q$	11664.bf.3d	$C_3^5:(C_2\times S_4)$	$C_2\times S_4$	$48$	48.a1	$243$	24.a1	$486$	$24$	$1$
11664.bf.4a	$4$	R		$1$	$\Q$	11664.bf.4a	$C_3^5:(C_2\times S_4)$	$S_3^2$	$36$	36.a1	$324$	36.a1	$324$	$36$	$1$
11664.bf.6a	$6$	R		$1$	$\Q$	11664.bf.6a	$C_3^5:(C_2\times S_4)$	$C_3^2:D_6$	$108$	108.a1	$108$	108.a1	$108$	$108$	$1$
11664.bf.6b	$6$	R		$1$	$\Q$	11664.bf.6b	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6c	$6$	R		$1$	$\Q$	11664.bf.6c	$C_3^5:(C_2\times S_4)$	$S_3\times S_4$	$144$	144.a1	$81$	144.a1	$81$	$144$	$1$
11664.bf.6d	$6$	R		$1$	$\Q$	11664.bf.6d	$C_3^5:(C_2\times S_4)$	$C_3^2:D_6$	$108$	108.a1	$108$	108.a1	$108$	$108$	$1$
11664.bf.6e	$6$	R		$1$	$\Q$	11664.bf.6e	$C_3^5:(C_2\times S_4)$	$S_3\times S_4$	$144$	144.a1	$81$	144.a1	$81$	$144$	$1$
11664.bf.6f	$6$	R		$1$	$\Q$	11664.bf.6f	$C_3^5:(C_2\times S_4)$	$C_6^2:D_6$	$432$	432.a1	$27$	432.a1	$27$	$432$	$1$
11664.bf.6g	$6$	R		$1$	$\Q$	11664.bf.6g	$C_3^5:(C_2\times S_4)$	$C_6^2:D_6$	$432$	432.a1	$27$	432.a1	$27$	$432$	$1$
11664.bf.6h	$6$	R		$1$	$\Q$	11664.bf.6h	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6i	$6$	R		$1$	$\Q$	11664.bf.6i	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.6j	$6$	R		$1$	$\Q$	11664.bf.6j	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.6k1	$6$	R		$12$	$\Q(\sqrt{3}) $	11664.bf.6k	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6k2	$6$	R		$12$	$\Q(\sqrt{3}) $	11664.bf.6k	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6l1	$6$	R		$12$	$\Q(\sqrt{3}) $	11664.bf.6l	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.6l2	$6$	R		$12$	$\Q(\sqrt{3}) $	11664.bf.6l	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.8a	$8$	R		$1$	$\Q$	11664.bf.8a	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.8b	$8$	R		$1$	$\Q$	11664.bf.8b	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.8c	$8$	R		$1$	$\Q$	11664.bf.8c	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.8d	$8$	R		$1$	$\Q$	11664.bf.8d	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.8e	$8$	R		$1$	$\Q$	11664.bf.8e	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.8f	$8$	R		$1$	$\Q$	11664.bf.8f	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.12a	$12$	R		$1$	$\Q$	11664.bf.12a	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.12b	$12$	R		$1$	$\Q$	11664.bf.12b	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.12c	$12$	R	✓	$1$	$\Q$	11664.bf.12c	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12d	$12$	R		$1$	$\Q$	11664.bf.12d	$C_3^5:(C_2\times S_4)$	$C_6^2:D_6$	$432$	432.a1	$27$	432.a1	$27$	$432$	$1$
11664.bf.12e	$12$	R		$1$	$\Q$	11664.bf.12e	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.12f	$12$	R		$1$	$\Q$	11664.bf.12f	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.12g	$12$	R		$1$	$\Q$	11664.bf.12g	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.12h	$12$	R		$1$	$\Q$	11664.bf.12h	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.12i	$12$	R	✓	$1$	$\Q$	11664.bf.12i	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12j1	$12$	R	✓	$12$	$\Q(\sqrt{3}) $	11664.bf.12j	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12j2	$12$	R	✓	$12$	$\Q(\sqrt{3}) $	11664.bf.12j	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12k1	$12$	R		$12$	$\Q(\sqrt{3}) $	11664.bf.12k	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.12k2	$12$	R		$12$	$\Q(\sqrt{3}) $	11664.bf.12k	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.16a	$16$	R		$1$	$\Q$	11664.bf.16a	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.16b	$16$	R		$1$	$\Q$	11664.bf.16b	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.16c	$16$	R		$1$	$\Q$	11664.bf.16c	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.24a	$24$	R		$1$	$\Q$	11664.bf.24a	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Degree	Type	Faithful	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
11664.bf.1a	$1$	R		$1$	\(\Q\)	11664.bf.1a	$C_3^5:(C_2\times S_4)$	$C_1$	$1$	1.a1	$11664$	1.a1	$11664$	$1$	$1$
11664.bf.1b	$1$	R		$1$	\(\Q\)	11664.bf.1b	$C_3^5:(C_2\times S_4)$	$C_2$	$2$	2.c1	$5832$	1.a1	$11664$	$1$	$1$
11664.bf.1c	$1$	R		$1$	\(\Q\)	11664.bf.1c	$C_3^5:(C_2\times S_4)$	$C_2$	$2$	2.b1	$5832$	1.a1	$11664$	$1$	$1$
11664.bf.1d	$1$	R		$1$	\(\Q\)	11664.bf.1d	$C_3^5:(C_2\times S_4)$	$C_2$	$2$	2.a1	$5832$	1.a1	$11664$	$1$	$1$
11664.bf.2a	$2$	R		$1$	\(\Q\)	11664.bf.2a	$C_3^5:(C_2\times S_4)$	$S_3$	$6$	6.b1	$1944$	6.b1	$1944$	$6$	$1$
11664.bf.2b	$2$	R		$1$	\(\Q\)	11664.bf.2b	$C_3^5:(C_2\times S_4)$	$S_3$	$6$	6.a1	$1944$	6.a1	$1944$	$6$	$1$
11664.bf.2c	$2$	R		$1$	\(\Q\)	11664.bf.2c	$C_3^5:(C_2\times S_4)$	$D_6$	$12$	12.a1	$972$	6.a1	$1944$	$6$	$1$
11664.bf.2d	$2$	R		$1$	\(\Q\)	11664.bf.2d	$C_3^5:(C_2\times S_4)$	$D_6$	$12$	12.b1	$972$	6.b1	$1944$	$6$	$1$
11664.bf.3a	$3$	R		$1$	\(\Q\)	11664.bf.3a	$C_3^5:(C_2\times S_4)$	$S_4$	$24$	24.a1	$486$	24.a1	$486$	$24$	$1$
11664.bf.3b	$3$	R		$1$	\(\Q\)	11664.bf.3b	$C_3^5:(C_2\times S_4)$	$S_4$	$24$	24.a1	$486$	24.a1	$486$	$24$	$1$
11664.bf.3c	$3$	R		$1$	\(\Q\)	11664.bf.3c	$C_3^5:(C_2\times S_4)$	$C_2\times S_4$	$48$	48.a1	$243$	24.a1	$486$	$24$	$1$
11664.bf.3d	$3$	R		$1$	\(\Q\)	11664.bf.3d	$C_3^5:(C_2\times S_4)$	$C_2\times S_4$	$48$	48.a1	$243$	24.a1	$486$	$24$	$1$
11664.bf.4a	$4$	R		$1$	\(\Q\)	11664.bf.4a	$C_3^5:(C_2\times S_4)$	$S_3^2$	$36$	36.a1	$324$	36.a1	$324$	$36$	$1$
11664.bf.6a	$6$	R		$1$	\(\Q\)	11664.bf.6a	$C_3^5:(C_2\times S_4)$	$C_3^2:D_6$	$108$	108.a1	$108$	108.a1	$108$	$108$	$1$
11664.bf.6b	$6$	R		$1$	\(\Q\)	11664.bf.6b	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6c	$6$	R		$1$	\(\Q\)	11664.bf.6c	$C_3^5:(C_2\times S_4)$	$S_3\times S_4$	$144$	144.a1	$81$	144.a1	$81$	$144$	$1$
11664.bf.6d	$6$	R		$1$	\(\Q\)	11664.bf.6d	$C_3^5:(C_2\times S_4)$	$C_3^2:D_6$	$108$	108.a1	$108$	108.a1	$108$	$108$	$1$
11664.bf.6e	$6$	R		$1$	\(\Q\)	11664.bf.6e	$C_3^5:(C_2\times S_4)$	$S_3\times S_4$	$144$	144.a1	$81$	144.a1	$81$	$144$	$1$
11664.bf.6f	$6$	R		$1$	\(\Q\)	11664.bf.6f	$C_3^5:(C_2\times S_4)$	$C_6^2:D_6$	$432$	432.a1	$27$	432.a1	$27$	$432$	$1$
11664.bf.6g	$6$	R		$1$	\(\Q\)	11664.bf.6g	$C_3^5:(C_2\times S_4)$	$C_6^2:D_6$	$432$	432.a1	$27$	432.a1	$27$	$432$	$1$
11664.bf.6h	$6$	R		$1$	\(\Q\)	11664.bf.6h	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6i	$6$	R		$1$	\(\Q\)	11664.bf.6i	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.6j	$6$	R		$1$	\(\Q\)	11664.bf.6j	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.6k1	$6$	R		$12$	\(\Q(\sqrt{3}) \)	11664.bf.6k	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6k2	$6$	R		$12$	\(\Q(\sqrt{3}) \)	11664.bf.6k	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.6l1	$6$	R		$12$	\(\Q(\sqrt{3}) \)	11664.bf.6l	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.6l2	$6$	R		$12$	\(\Q(\sqrt{3}) \)	11664.bf.6l	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.8a	$8$	R		$1$	\(\Q\)	11664.bf.8a	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.8b	$8$	R		$1$	\(\Q\)	11664.bf.8b	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.8c	$8$	R		$1$	\(\Q\)	11664.bf.8c	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.8d	$8$	R		$1$	\(\Q\)	11664.bf.8d	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.8e	$8$	R		$1$	\(\Q\)	11664.bf.8e	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.8f	$8$	R		$1$	\(\Q\)	11664.bf.8f	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.12a	$12$	R		$1$	\(\Q\)	11664.bf.12a	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.12b	$12$	R		$1$	\(\Q\)	11664.bf.12b	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.12c	$12$	R	✓	$1$	\(\Q\)	11664.bf.12c	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12d	$12$	R		$1$	\(\Q\)	11664.bf.12d	$C_3^5:(C_2\times S_4)$	$C_6^2:D_6$	$432$	432.a1	$27$	432.a1	$27$	$432$	$1$
11664.bf.12e	$12$	R		$1$	\(\Q\)	11664.bf.12e	$C_3^5:(C_2\times S_4)$	$C_3^3:S_4$	$648$	648.a1	$18$	648.a1	$18$	$648$	$1$
11664.bf.12f	$12$	R		$1$	\(\Q\)	11664.bf.12f	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.12g	$12$	R		$1$	\(\Q\)	11664.bf.12g	$C_3^5:(C_2\times S_4)$	$C_2\times C_3^3:S_4$	$1296$	1296.a1	$9$	648.a1	$18$	$648$	$1$
11664.bf.12h	$12$	R		$1$	\(\Q\)	11664.bf.12h	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.12i	$12$	R	✓	$1$	\(\Q\)	11664.bf.12i	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12j1	$12$	R	✓	$12$	\(\Q(\sqrt{3}) \)	11664.bf.12j	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12j2	$12$	R	✓	$12$	\(\Q(\sqrt{3}) \)	11664.bf.12j	$C_3^5:(C_2\times S_4)$	$C_3^5:(C_2\times S_4)$	$11664$	11664.a1	$1$	11664.a1	$1$	$11664$	$1$
11664.bf.12k1	$12$	R		$12$	\(\Q(\sqrt{3}) \)	11664.bf.12k	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.12k2	$12$	R		$12$	\(\Q(\sqrt{3}) \)	11664.bf.12k	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.16a	$16$	R		$1$	\(\Q\)	11664.bf.16a	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.16b	$16$	R		$1$	\(\Q\)	11664.bf.16b	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.16c	$16$	R		$1$	\(\Q\)	11664.bf.16c	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$
11664.bf.24a	$24$	R		$1$	\(\Q\)	11664.bf.24a	$C_3^5:(C_2\times S_4)$	$S_3\times C_3^3:S_4$	$3888$	3888.a1	$3$	3888.a1	$3$	$3888$	$1$