Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D2348 |
| Fitting | C22×C4×C587 ⋊ C2 |
| Sylow | C587 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D587 |
| commutator, cosocle | C2×C587 | C24 |
| Frattini | C2 | C23×D587 |
| Fitting | C22×C4×C587 | C2 |
| socle | C23×C587 | C22 |
| hypercenter | C22×C4 | D587 |
| hypocenter | C587 | C22×D4 |
| LCS | G ▷ C2×C587 ▷ C587 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
4708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49176958, #49176981, #49176982, … |
| maximal normal subgroup of | #49176958, #49176981, #49176982, … |
| maximal quotient of | C22×(C2×D587)⋊C4, C22×C4⋊Dic587, C2×C4×D2348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 184);