Finite Group DatabasebetaFinite Group Databasebeta| order | 27996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D2333 |
| unambiguous semidirect product | C2333⋊(C22×C3) |
| unambiguous semidirect product | (C2×C2333)⋊(C2×C3) |
| Fitting, socle | C2×C3×C2333 ⋊ C2 |
| derived, Sylow | C2333 ⋊ C22×C3 |
| Hall | C3×C2333 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D2333 |
| commutator, cosocle, hypocenter | C2333 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C2333 | C2 |
| LCS | G ▷ C2333 | |
| UCS | C1 ◁ C2×C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13998 |
7008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27996, 10);