Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C25⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C2×C25)⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C2×C23⋊C11)⋊D25 |
| unambiguous semidirect product | (C2×D575)⋊C11 |
| Fitting | C2×C23×C25 ⋊ C2×C11 |
| derived, Hall | C23×C25 ⋊ C22×C11 |
| Hall | C25×C23⋊C11 ⋊ C22 |
| Hall | C2×D575 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×AGL(1,𝔽23) |
| Sylow | C23 ⋊ C2×C11×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C25⋊AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23×C25 | C22×C11 |
| Frattini | C5 | C2×C5⋊AGL(1,𝔽23) |
| Fitting | C2×C23×C25 | C2×C11 |
| socle | C2×C5×C23 | D5×C11 |
| LCS | G ▷ C23×C25 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1150 |
358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 22);