Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C11⋊(C23⋊#1044) |
| unambiguous semidirect product | C23⋊(C11⋊#1044) |
| Fitting, socle, derived, Hall | C52×C11×C23 ⋊ C4 |
| Hall | C52×C23 ⋊ Dic11 |
| Hall | C52×C11 ⋊ Dic23 |
| Hall | C11×C23 ⋊ #1044 |
| Sylow | C52 ⋊ Dic253 |
| Sylow | C23 ⋊ C11⋊#1044 |
| Sylow | C11 ⋊ C23⋊#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11×C23 | C4 |
| prime radical, cosocle | C11×C23×C5⋊D5 | C2 |
| LCS | G ▷ C52×C11×C23 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2530 |
Polycyclic presentation:
2^2,5^2,11,23|a^2=b,c^a=c^2,d^a=d^3,e^a=e^10,f^a=f^22,c^b=c^4,d^b=d^41774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 151);