Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C181 · Schur multiplier (H2) = C24×C4 |
| direct product | #1434×C181 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C181 | C23 |
| commutator | C22 | C2×C42×C181 |
| Frattini, cosocle | C24 | C23×C181 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C181 ◁ G | |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
10136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 166);