Finite Group DatabasebetaFinite Group Databasebeta| order | 976 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic61 |
| derived, Sylow | C61 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D61 |
| commutator, hypocenter | C61 | C42 |
| Frattini | C22 | C2×D61 |
| Fitting | C2×C4×C61 | C2 |
| socle, prime radical, cosocle | C22×C61 | C22 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Dic61, #14519687, #14519703, … |
| maximal normal subgroup of | C8×Dic61, #14519687, #14519703, … |
| maximal quotient of | #14519684, C8×Dic61, C4×#92418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(976, 11);