Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C83⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C2×C83)⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C2×C5⋊D415)⋊C3 |
| Fitting, socle | C2×C52×C83 ⋊ C2×C3 |
| derived, Hall | C52×C83 ⋊ C22×C3 |
| Hall | C2×C5⋊D415 ⋊ C3 |
| Hall | C52⋊C3×C83 ⋊ C22 |
| Sylow | C83 ⋊ C2×(C5⋊D5)⋊C3 |
| Hall | C52⋊C3 ⋊ C2×D83 |
| Sylow | C52 ⋊ C2×C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C83⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C52×C83 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C83 | C2×C3 |
| LCS | G ▷ C52×C83 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2490 |
922 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 61);