Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C181 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#124×C181 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C181 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C181 |
| prime radical | C23×D4×C181 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C181 ◁ G | |
1880 conjugacy classes of subgroups; only the 952 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 952 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11584 |
10136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 2168);