Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#15667734 |
| Fitting | C8×C353 ⋊ C8 |
| derived, Sylow | C353 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #15667734 |
| commutator, hypocenter | C353 | C82 |
| Frattini | C4 | C2×#15667734 |
| Fitting | C8×C353 | C8 |
| socle | C2×C353 | C4×C8 |
| prime radical | C2×D353 | C42 |
| cosocle | C4×#13083443 | C22 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2824 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 1632);