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 | (C7⋊D7)⋊D43 ⋊ C3 |
| Hall | #20263479 ⋊ C22 |
| Sylow | C72 ⋊ C2×D43⋊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:
(1,2,8)(3,12,24)(4,6,13)(5,16,7)(9,25,36)(10,26,23)(11,29,15)(14,33,20)(17,18,37)(19,35,28)(21,34,22)(27,43,30)(31,42,39)(32,38,40)(44,45,46,50,47,49)(52,55,56,53,54,57);(2,3)(4,6)(5,9)(7,8)(10,14)(11,17)(12,20)(13,22)(15,24)(16,26)(18,27)(19,23)(21,30)(25,32)(28,36)(29,38)(31,40)(33,39)(34,37)(35,41)(42,43)(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,f^a=f^42,d^b=d^6,e^b=e^6,d^c=d^2,e^c=e^2,f^c=f^36201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25284, 268);