Finite Group DatabasebetaFinite Group Databasebeta| order | 19288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D2411 |
| unambiguous semidirect product | C2411⋊C23 |
| unambiguous semidirect product | (C2×C2411)⋊C22 |
| Fitting, socle | C22×C2411 ⋊ C2 |
| derived, Sylow | C2411 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D2411 |
| commutator, cosocle, hypocenter | C2411 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C2411 | C2 |
| LCS | G ▷ C2411 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9644 |
4828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D2411)⋊C4, C2×C4×D2411, D4×D2411, … |
| maximal normal subgroup of | (C2×D2411)⋊C4, C2×C4×D2411, D4×D2411, … |
| maximal quotient of | C2×C4×D2411, C22×Dic2411, D4×D2411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19288, 12);