Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×C7⋊Dic371 |
| derived, Hall | C72×C53 ⋊ C3×C4 |
| Hall | C3×C72×C53 ⋊ C4 |
| Hall | C3×C53 ⋊ C7⋊Dic7 |
| Hall | C3×C72 ⋊ Dic53 |
| Sylow | C53 ⋊ C3×C7⋊Dic7 |
| Sylow | C72 ⋊ C3×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C7⋊D371 |
| commutator, hypocenter | C72×C53 | C3×C4 |
| Frattini | C2 | C3×C7⋊D371 |
| Fitting, socle, prime radical | C2×C3×C72×C53 | C2 |
| cosocle | C2×C72×C53 | C2×C3 |
| LCS | G ▷ C72×C53 | |
| UCS | C1 ◁ C2×C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31164 |
7800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 70);