Finite Group DatabasebetaFinite Group Databasebeta| order | 24100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#11757210 |
| Fitting, Hall | C25×C241 ⋊ C4 |
| derived, Sylow | C241 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #11757210 |
| commutator, hypocenter | C241 | C4×C25 |
| Frattini | C5 | C5×#11757210 |
| Fitting | C25×C241 | C4 |
| socle | C5×C241 | C4×C5 |
| prime radical, cosocle | C5×D241 | C2×C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6025 |
1600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24100, 11);