Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C8×#64408 |
| Fitting | C23×C8×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C23×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #64408 |
| commutator, hypocenter | C73 | C23×C4×C8 |
| Frattini | C4 | C24×#64408 |
| Fitting | C23×C8×C73 | C4 |
| socle | C24×C73 | C42 |
| prime radical | C24×D73 | C2×C4 |
| cosocle | C4×D73 | C25 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C23×C8 | |
4638 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
1408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1114642);