Finite Group DatabasebetaFinite Group Databasebeta| order | 25270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C7⋊((C19⋊D19)⋊C5) |
| unambiguous semidirect product | (C7⋊(C19⋊D19))⋊C5 |
| Fitting, socle, derived, Hall | C7×C192 ⋊ C2×C5 |
| Hall | C7×C192⋊C5 ⋊ C2 |
| Hall | C7⋊(C19⋊D19) ⋊ C5 |
| Hall | C192⋊C5 ⋊ D7 |
| Sylow | C192 ⋊ C5×D7 |
| Sylow | C7 ⋊ (C19⋊D19)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C192 | C2×C5 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 102 |
| transitive degree | μt(G) = 665 |
A minimal faithful permutation representation — 2 generators on 102 points:
(1,2,4,9,21)(3,16,17,53,71,7,6,41,43,50)(5,30,32,82,88,12,13,60,61,95)(8,45,46,87,81,19,18,70,73,78)(10,55,56,90,66,24,25,83,75,36)(11,23,58,74,37,28,29,54,48,68)(14,33,64,84,20,34,35,63,85,47)(15,65,69,76,77,38,39,62,49,92)(22,79,80,42,27,51,52,94,31,26)(40,44,59,89,93,67,57,72,86,91)(97,98)(99,100)(101,102);(1,3,8,20,48,75,91,92,95,80,94,88,77,93,90,74,47,19,7)(2,5,14,36,67,45,31,6,15,37,68,38,16,42,18,40,66,34,12)(4,10,26,28,17,44,13,33,46,65,39,70,35,30,57,41,11,27,24)(9,22,53,60,87,62,63,72,23,25,55,29,59,64,69,73,32,43,51)(21,49,56,78,79,85,54,82,71,86,89,50,61,58,84,52,81,83,76)(96,97,99,101,102,100,98)Polycyclic presentation:
2,5,7,19^2|c^a=c^6,d^a=d^18,e^a=e^18,d^b=d^12e^2,e^b=d^18e^11277 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25270, 14);