Finite Group DatabasebetaFinite Group Databasebeta| order | 27275 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C1091⋊C5 |
| unambiguous semidirect product | C1091⋊C52 |
| unambiguous semidirect product | (C5×C1091)⋊C5 |
| Fitting, socle | C5×C1091 ⋊ C5 |
| derived, Sylow | C1091 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C1091⋊C5 |
| commutator, cosocle, hypocenter | C1091 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1091 | C5 |
| LCS | G ▷ C1091 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5455 |
1115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27275, 3);