Finite Group DatabasebetaFinite Group Databasebeta| order | 12462 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C67 ⋊ C2×C3 |
| Hall | #20262033 ⋊ C2 |
| Hall | C31×D67 ⋊ C3 |
| Hall | D67 ⋊ C31⋊C3 |
| Sylow | C67 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C67 | C2×C3 |
| LCS | G ▷ C31×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 98 |
| transitive degree | μt(G) = 2077 |
A minimal faithful permutation representation — 2 generators on 98 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,55,54,40,49,65)(34,62,63,50,48,56)(37,42,61,51,52,57)(53,60,66,58,64,67)(69,70,72)(71,74,79)(73,77,76)(75,81,88)(78,84,86)(80,82,83)(85,91,95)(87,92,93)(89,96,90)(94,97,98);(1,2,5,11,19,32,36,10,16,24,38,54,66,64,31,48,55,57,59,63,28,43,44,27,42,58,51,35,22,7,6,12,21,34,50,33,20,4,8,13,23,37,53,52,18,29,39,41,56,47,61,49,62,46,60,67,65,45,15,26,14,25,40,30,17,9,3)(68,69,71,75,82,72,76,83,90,96,79,86,93,81,89,88,95,98,91,74,80,87,94,97,84,70,73,78,85,92,77)Polycyclic presentation:
2,3,31,67|d^a=d^66,c^b=c^25,d^b=d^37367 conjugacy classes — view the full character table.
| maximal subgroup of | #27159573⋊C2, C2×#27159573, C31⋊C3×D67⋊C3, … |
| maximal normal subgroup of | #27159573⋊C2, C2×#27159573, C31⋊C3×D67⋊C3, … |
| maximal quotient of | #38735403, C2×#27159573, #49153271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12462, 15);