Finite Group DatabasebetaFinite Group Databasebeta| order | 15276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#21439413 |
| Fitting, socle | C2×C19×C67 ⋊ C2×C3 |
| derived, Hall | C19×C67 ⋊ C22×C3 |
| Hall | C2×D1273 ⋊ C3 |
| Hall | #16838390 ⋊ C22 |
| Sylow | C67 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #21439413 |
| commutator, cosocle, hypocenter | C19×C67 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C67 | C2×C3 |
| LCS | G ▷ C19×C67 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2546 |
436 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15276, 33);