Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C7 |
| direct product | C32×C7⋊Dic133 |
| derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | C32×C72×C19 ⋊ C4 |
| Hall | C32×C72 ⋊ Dic19 |
| Hall | C32×C19 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C32×Dic19 |
| Sylow | C19 ⋊ C32×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C7⋊D133 |
| commutator, hypocenter | C72×C19 | C32×C4 |
| Frattini | C2 | C32×C7⋊D133 |
| Fitting, socle, prime radical | C2×C32×C72×C19 | C2 |
| cosocle | C2×C72×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2×C32 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33516 |
8406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 769);