Finite Group DatabasebetaFinite Group Databasebeta| order | 6076 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic31 |
| unambiguous semidirect product | C31⋊(C4×C72) |
| derived, Sylow | C31 ⋊ C4×C72 |
| Hall | C72×C31 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D31 |
| commutator, hypocenter | C31 | C4×C72 |
| Frattini | C2 | C72×D31 |
| Fitting, socle | C2×C72×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C72 | |
60 conjugacy classes of subgroups.
1666 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×(C31⋊C3)⋊C4, C7×#14579595, C7×#14579596, … |
| maximal normal subgroup of | C72×(C31⋊C3)⋊C4, C7×#14579595, C7×#14579596, … |
| maximal quotient of | C3×C72×Dic31, C72×Dic93, C72×Dic155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6076, 11);