Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D64×D73 |
| Fitting | C73×D64 ⋊ C2 |
| Sylow | C73 ⋊ C2×D64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D73 |
| commutator, cosocle | C32×C73 | C23 |
| Frattini | C32 | C22×D73 |
| Fitting | C73×D64 | C2 |
| socle | C2×C73 | C2×D32 |
| hypercenter | D64 | D73 |
| hypocenter | C73 | C2×D64 |
| LCS | G ▷ C32×C73 ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ D64 | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 90609);