Finite Group DatabasebetaFinite Group Databasebeta| order | 15276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#16838389 |
| Fitting, socle, Hall | C22×C19×C67 ⋊ C3 |
| derived, Hall | C19×C67 ⋊ C22×C3 |
| Hall | C22×C67 ⋊ C19⋊C3 |
| Hall | C22×C19 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C22×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #16838389 |
| commutator, cosocle, hypocenter | C19×C67 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C67 | C3 |
| LCS | G ▷ C19×C67 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5092 |
1708 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15276, 54);