Finite Group DatabasebetaFinite Group Databasebeta| order | 6076 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic217 |
| unambiguous semidirect product | C7⋊(C7×Dic31) |
| unambiguous semidirect product | C31⋊(C7×Dic7) |
| derived | C7×C31 ⋊ C4×C7 |
| Hall | C72×C31 ⋊ C4 |
| Sylow | C72 ⋊ Dic31 |
| Sylow | C31 ⋊ C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D217 |
| commutator, hypocenter | C7×C31 | C4×C7 |
| Frattini | C2 | C7×D217 |
| Fitting, socle | C2×C72×C31 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
1540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#14579601, C7×#14579602, C7×ΓL(1,𝔽8)⋊Dic31, … |
| maximal normal subgroup of | C7×#14579601, C7×#14579602, C7×ΓL(1,𝔽8)⋊Dic31, … |
| maximal quotient of | C3×C7×Dic217, C7×Dic651, C7×Dic1085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6076, 13);