Finite Group DatabasebetaFinite Group Databasebeta| order | 13542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C61 ⋊ C2×C3 |
| Hall | #20270133 ⋊ C2 |
| Hall | C37×D61 ⋊ C3 |
| Hall | D61 ⋊ C37⋊C3 |
| Sylow | C61 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C61 | C2×C3 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 2257 |
A minimal faithful permutation representation — 2 generators on 98 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,40)(12,26,22,20,16,13)(19,45,46,30,31,56)(21,43,44,32,29,37)(23,25,42,34,35,38)(33,58,59,48,47,54)(36,41,57,50,49,55)(39,61,60,52,53,51)(63,64,66)(65,68,73)(67,71,70)(69,75,82)(72,77,79)(74,80,76)(78,85,89)(81,87,86)(83,90,84)(88,93,94)(91,95,92)(96,98,97);(1,2,5,11,19,31,47,53,55,56,50,34,22,7,6,12,21,33,49,18,29,38,40,54,60,44,15,26,14,25,39,52,35,10,16,24,37,51,59,28,42,43,27,41,48,32,20,4,8,13,23,36,46,57,61,58,45,30,17,9,3)(62,63,65,69,75,83,91,96,95,80,66,70,76,84,85,68,74,81,88,90,73,79,86,92,93,77,64,67,72,78,82,89,94,97,98,87,71)Polycyclic presentation:
2,3,37,61|d^a=d^60,c^b=c^26,d^b=d^47400 conjugacy classes — view the full character table.
| maximal subgroup of | #41028941, #27214370⋊C2, #41028951, … |
| maximal normal subgroup of | #41028941, #27214370⋊C2, #41028951, … |
| maximal quotient of | #41028916, C2×#27214370 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13542, 15);