Finite Group DatabasebetaFinite Group Databasebeta| order | 6076 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C7 |
| direct product | C31×#5997 |
| Fitting, socle, Hall | C72×C31 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #5997 |
| commutator, hypocenter | C72 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C72×C31 | C4 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C31 | |
28 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#10596885, C31×#5997⋊C3, #32912196, … |
| maximal normal subgroup of | C31×#5997⋊C3, #32912196, #32912197, … |
| maximal quotient of | C3×C31×#5997, C31×C3⋊#5997, C5×C31×#5997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6076, 22);