Finite Group DatabasebetaFinite Group Databasebeta| order | 33810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C23×#64418 |
| Fitting, socle, Hall | C5×C72×C23 ⋊ D3 |
| derived, Hall | #3862 ⋊ C2×C5×C23 |
| Hall | C5×C23×#3862 ⋊ C2 |
| Hall | C23×#3862 ⋊ C2×C5 |
| Hall | C72×C23 ⋊ C5×D3 |
| Hall | C5×#3862 ⋊ C2×C23 |
| Hall | C5×C72 ⋊ D3×C23 |
| Sylow | C72 ⋊ C5×D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | #64418 |
| commutator, cosocle, hypocenter | #3862 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C23 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C5×C23 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1610 |
2300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33810, 26);