Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×#15668452 |
| derived, Sylow | C181 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #10624382 |
| commutator, hypocenter | C181 | C8×C16 |
| Frattini | C42 | C2×#10624382 |
| Fitting | C4×C8×C181 | C4 |
| socle, prime radical | C22×C181 | C4×C8 |
| cosocle | C4×#13089678 | C22 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C4×C8 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
1568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19420);