Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D584 |
| Fitting | C24×C8×C73 ⋊ C2 |
| Sylow | C73 ⋊ C24×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | D292 |
| commutator, cosocle | C4×C73 | C26 |
| Frattini | C4 | C25×D73 |
| Fitting | C24×C8×C73 | C2 |
| socle | C25×C73 | D4 |
| hypercenter | C24×C8 | D73 |
| hypocenter | C73 | C24×D8 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C25 ◁ C24×C4 ◁ C24×C8 | |
15454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
4720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1083343);