Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | Dic29×C52⋊C9 |
| unambiguous semidirect product | (C52×Dic29)⋊C9 |
| derived, Hall | C52×C29 ⋊ C4×C9 |
| Hall | C29×C52⋊C9 ⋊ C4 |
| Hall | C52×Dic29 ⋊ C9 |
| Sylow | C29 ⋊ C4×C52⋊C9 |
| Sylow | C52 ⋊ C9×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D29×C52⋊C3 |
| commutator, hypocenter | C52×C29 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C29 | C2×C3 |
| LCS | G ▷ C52×C29 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5220 |
1056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 54);