Finite Group DatabasebetaFinite Group Databasebeta| order | 25284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C43 ⋊ C22×C3 |
| Hall | D72×C43 ⋊ C3 |
| Hall | #20263480 ⋊ C22 |
| Hall | D72 ⋊ C43⋊C3 |
| Sylow | C72 ⋊ C22×C43⋊C3 |
| Sylow | C43 ⋊ #64423⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C43 | C22×C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 602 |
A minimal faithful permutation representation — 2 generators on 57 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,30)(18,26,31)(21,29,28)(23,32,25)(27,36,38)(33,39,37)(34,40,35)(41,43,42)(44,45,50)(47,48,49)(52,55,56,53,54,57);(1,2,4,8,15,17,3,6,11,18,27,26,7,13,21,30,38,36,14,23,33,40,22,31,24,34,41,43,32,12,19,28,37,42,39,20,5,9,16,25,35,29,10)(45,46)(47,48)(49,50)(51,52,54,57,56,55,53)Polycyclic presentation:
2^2,3,7^2,43|d^a=d^6,e^b=e^6,d^c=d^2,e^c=e^2,f^c=f^6369 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 271);