Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C181 · Schur multiplier (H2) = C214 |
| direct product | C22×H(5,𝔽2)×C181 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C181 | C24 |
| commutator, Frattini, cosocle | C2 | C26×C181 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C181 ◁ G | |
6560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
12308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 2323);