Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C11 |
| direct product | C23×#13089721 |
| Fitting, socle, Hall | C112×C23 ⋊ Dic3 |
| derived, Hall | C112⋊C3 ⋊ C4×C23 |
| Hall | C23×C112⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ Dic3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #13089721 |
| commutator, hypocenter | C112⋊C3 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | Dic3 |
| prime radical | C23×(C11⋊D11)⋊C3 | C2 |
| cosocle | (C11⋊D11)⋊C3 | C2×C23 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 79);