Finite Group DatabasebetaFinite Group Databasebeta| order | 26700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C89⋊#3874 |
| unambiguous semidirect product | (C2×C89)⋊#3874 |
| Fitting, socle | C2×C52×C89 ⋊ D3 |
| derived, Hall | C52⋊C3×C89 ⋊ C22 |
| Hall | C52×C89 ⋊ C2×D3 |
| Sylow | C89 ⋊ C2×#3874 |
| Hall | C52⋊C3 ⋊ C2×D89 |
| Sylow | C52 ⋊ C2×D267 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C89⋊#3874 |
| commutator, cosocle, hypocenter | C52⋊C3×C89 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C89 | D3 |
| LCS | G ▷ C52⋊C3×C89 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2670 |
994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26700, 73);