Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C44 · Schur multiplier (H2) = C46 |
| direct product | C43×#64408 |
| Fitting | C43×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C44 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #64408 |
| commutator, hypocenter | C73 | C44 |
| Frattini | C23 | C23×#64408 |
| Fitting | C43×C73 | C4 |
| socle | C23×C73 | C23×C4 |
| prime radical, cosocle | C23×D73 | C24 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C43 | |
3966 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, 1098151);