Finite Group DatabasebetaFinite Group Databasebeta| order | 2324 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C83 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×C83 |
| unambiguous semidirect product | C7⋊(C22×C83) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C83) |
| Fitting, socle | C2×C7×C83 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C83 |
| Hall | C7×C83 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | D7 |
| commutator, cosocle, hypocenter | C7 | C22×C83 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C83 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C83 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1162 |
830 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D7×C83, C2×D35×C83, C2×C5×D7×C83, … |
| maximal normal subgroup of | C2×C5×D7×C83, C2×C7×D7×C83, C2×C11×D7×C83, … |
| maximal quotient of | D5×D7×C83, C2×D35×C83, C2×C5×D7×C83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2324, 8);