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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (displaying both matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
3201186852864000.a.1.a1.a1 $A_{18}$ $2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ ✓ ✓ $A_{18}$ $2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ $C_1$ $1$ ✓ ✓
3201186852864000.a.3201186852864000.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $A_{18}$ $2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$ $A_{18}$ $2^{15} \cdot 3^{8} \cdot 5^{3} \cdot 7^{2} \cdot 11 \cdot 13 \cdot 17$
  displayed columns for results