Finite Group DatabasebetaFinite Group Databasebeta| order | 30592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #400×D239 |
| Fitting | #400×C239 ⋊ C2 |
| Sylow | C239 ⋊ C2×#400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D239 |
| commutator, socle, cosocle | C23×C239 | C24 |
| Fitting | #400×C239 | C2 |
| prime radical | C23×D239 | C23 |
| hypercenter | #400 | D239 |
| hypocenter | C239 | C2×#400 |
| LCS | G ▷ C23×C239 ▷ C239 | |
| UCS | C1 ◁ C23 ◁ #400 | |
604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15296 |
2662 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30592, 7760);