Finite Group DatabasebetaFinite Group Databasebeta| order | 6076 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C7 |
| direct product | C31×C7⋊Dic7 |
| unambiguous semidirect product | C7⋊(Dic7×C31) |
| derived, Sylow | C72 ⋊ C4×C31 |
| Hall | C72×C31 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | C7⋊D7 |
| commutator, hypocenter | C72 | C4×C31 |
| Frattini | C2 | C31×C7⋊D7 |
| Fitting, socle | C2×C72×C31 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C31 | |
60 conjugacy classes of subgroups.
1612 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#10596874, #32912073, #32912074, … |
| maximal normal subgroup of | C31×#10596874, #32912073, #32912074, … |
| maximal quotient of | C3×C31×C7⋊Dic7, C31×C3⋊(C7⋊Dic7), C31×C7⋊Dic35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6076, 14);