Finite Group DatabasebetaFinite Group Databasebeta| order | 27100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5⋊D1355 |
| unambiguous semidirect product | (C2×C5)⋊D1355 |
| unambiguous semidirect product | (C2×C271)⋊(C5⋊D5) |
| Fitting, socle | C2×C52×C271 ⋊ C2 |
| derived, Hall | C52×C271 ⋊ C22 |
| Sylow | C271 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D271 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊D1355 |
| commutator, cosocle, hypocenter | C52×C271 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C271 | C2 |
| LCS | G ▷ C52×C271 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13550 |
6778 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27100, 51);