Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
| direct product | #4296×C7⋊Dic7 |
| derived, Hall | C72×C19 ⋊ C4×C9 |
| Hall | C72×#4296 ⋊ C4 |
| Hall | C19×C7⋊Dic7 ⋊ C9 |
| Sylow | C72 ⋊ C4×#4296 |
| Sylow | C19 ⋊ C9×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊D7×#4296 |
| commutator, hypocenter | C72×C19 | C4×C9 |
| Fitting, socle | C2×C72×C19 | C2×C9 |
| prime radical, cosocle | C2×C72×C19⋊C3 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3724 |
572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 605);