Finite Group DatabasebetaFinite Group Databasebeta| order | 1302 |
| isoclinism | isoclinic class of #10620252 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#10620252 |
| Fitting, socle, Hall | C2×C7×C31 ⋊ C3 |
| derived, Hall | C7×C31 ⋊ C2×C3 |
| Hall | C2×C31 ⋊ ΓL(1,𝔽8) |
| Sylow | C31 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C31⋊C3 |
| Sylow | C7 ⋊ C2×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10620252 |
| commutator, cosocle, hypocenter | C7×C31 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C31 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 434 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #14579595, #14579599, #14579601, … |
| maximal normal subgroup of | #14579595, #14579599, #14579601, … |
| maximal quotient of | C4×#10620252, C22×#10620252, C2×#14519869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1302, 15);