Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊AGL(1,𝔽23) |
| unambiguous semidirect product | ((C5⋊D5)⋊D23)⋊C11 |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽23))⋊D5 |
| Fitting, socle, derived, Hall | C52×C23 ⋊ C22×C11 |
| Hall | C52×C23⋊C11 ⋊ C22 |
| Hall | (C5⋊D5)⋊D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D52 |
| Sylow | C52 ⋊ C2×AGL(1,𝔽23) |
| Sylow | C23 ⋊ D52×C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C23 | C22×C11 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 230 |
Polycyclic presentation:
2^2,11,5^2,23|d^a=d^4,f^a=f^22,d^b=d^4,e^b=e^4,f^c=f^2190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 81);