Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C162 · Schur multiplier (H2) = C16 |
| direct product | C16×#11924040 |
| derived, Sylow | C73 ⋊ C162 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #10596842 |
| commutator, hypocenter | C73 | C162 |
| Frattini | C2×C8 | C2×#10596842 |
| Fitting | C2×C16×C73 | C8 |
| socle, prime radical | C22×C73 | C82 |
| cosocle | C8×#10596833 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C16 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116333);