Properties

Label 15T44
Order \(2430\)
n \(15\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $15$
Transitive number $t$ :  $44$
CHM label :  $[3^{5}:2]5$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,11)(2,7)(4,14)(5,10)(8,13), (1,4,7,10,13)(2,5,8,11,14)(3,6,9,12,15), (5,10,15)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
5:  $C_5$
6:  $S_3$
10:  $C_{10}$
30:  $S_3 \times C_5$
810:  15T33

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 5: $C_5$

Low degree siblings

15T44 x 15, 30T394 x 16, 45T253 x 8, 45T254 x 16, 45T255 x 32, 45T256 x 32, 45T257 x 64, 45T258 x 64

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 5,15,10)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 3,13, 8)( 5,15,10)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 3,13, 8)( 5,10,15)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 5,15,10)$
$ 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 5,10,15)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3,13, 8)( 5,15,10)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3,13, 8)( 5,10,15)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3, 8,13)( 5,15,10)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3, 8,13)( 5,10,15)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 3,13, 8)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 3,13, 8)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 3, 8,13)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $10$ $3$ $( 3, 8,13)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3,13, 8)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3,13, 8)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3, 8,13)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1,11, 6)( 3, 8,13)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1, 6,11)( 3,13, 8)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1, 6,11)( 3,13, 8)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1, 6,11)( 3, 8,13)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 1, 1, 1 $ $10$ $3$ $( 1, 6,11)( 3, 8,13)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 3 $ $2$ $3$ $( 1,11, 6)( 2,12, 7)( 3,13, 8)( 4,14, 9)( 5,15,10)$
$ 3, 3, 3, 3, 3 $ $10$ $3$ $( 1,11, 6)( 2,12, 7)( 3,13, 8)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 3 $ $10$ $3$ $( 1,11, 6)( 2,12, 7)( 3, 8,13)( 4,14, 9)( 5,10,15)$
$ 3, 3, 3, 3, 3 $ $10$ $3$ $( 1, 6,11)( 2,12, 7)( 3,13, 8)( 4,14, 9)( 5,10,15)$
$ 2, 2, 2, 2, 2, 1, 1, 1, 1, 1 $ $243$ $2$ $( 6,11)( 7,12)( 8,13)( 9,14)(10,15)$
$ 5, 5, 5 $ $81$ $5$ $( 1, 4, 7,10,13)( 2, 5, 8,11,14)( 3, 6, 9,12,15)$
$ 15 $ $162$ $15$ $( 1, 4, 7, 5, 8,11,14, 2,15, 3, 6, 9,12,10,13)$
$ 10, 5 $ $243$ $10$ $( 1, 4,12,10, 8, 6,14, 2, 5,13)( 3,11, 9, 7,15)$
$ 5, 5, 5 $ $81$ $5$ $( 1, 7,13, 4,10)( 2, 8,14, 5,11)( 3, 9,15, 6,12)$
$ 15 $ $162$ $15$ $( 1, 7,13, 4, 5,11, 2, 8,14,15, 6,12, 3, 9,10)$
$ 10, 5 $ $243$ $10$ $( 1,12, 3,14, 5, 6, 7, 8, 9,10)( 2,13, 4,15,11)$
$ 5, 5, 5 $ $81$ $5$ $( 1,13,10, 7, 4)( 2,14,11, 8, 5)( 3,15,12, 9, 6)$
$ 15 $ $162$ $15$ $( 1,13, 5, 2,14,11, 8,15,12, 9, 6, 3,10, 7, 4)$
$ 10, 5 $ $243$ $10$ $( 1, 8, 5, 2, 9,11,13,15, 7, 4)( 3,10,12,14, 6)$
$ 5, 5, 5 $ $81$ $5$ $( 1,10, 4,13, 7)( 2,11, 5,14, 8)( 3,12, 6,15, 9)$
$ 15 $ $162$ $15$ $( 1, 5,14, 8, 2,11,15, 9, 3,12, 6,10, 4,13, 7)$
$ 10, 5 $ $243$ $10$ $( 1,15,14,13,12,11, 5, 9, 3, 7)( 2, 6,10, 4, 8)$

Group invariants

Order:  $2430=2 \cdot 3^{5} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.