Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D587 |
| unambiguous semidirect product | C587⋊C25 |
| unambiguous semidirect product | (C2×C587)⋊C24 |
| Fitting, socle | C24×C587 ⋊ C2 |
| derived, Sylow | C587 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D587 |
| commutator, cosocle, hypocenter | C587 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C587 | C2 |
| LCS | G ▷ C587 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
4720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49176935, C2×C22⋊C4×D587, C22×(C2×D587)⋊C4, … |
| maximal normal subgroup of | #49176935, C2×C22⋊C4×D587, C22×(C2×D587)⋊C4, … |
| maximal quotient of | C23×C4×D587, C24×Dic587, C22×D4×D587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 195);