Finite Group DatabasebetaFinite Group Databasebeta| order | 7564 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic61 |
| derived, Sylow | C61 ⋊ C4×C31 |
| Hall | C31×C61 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D61 |
| commutator, hypocenter | C61 | C4×C31 |
| Frattini | C2 | C31×D61 |
| Fitting, socle | C2×C31×C61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C31 | |
12 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C31×Dic61, C31×Dic183, C31×Dic61⋊C3, … |
| maximal normal subgroup of | C3×C31×Dic61, C31×Dic61⋊C3, C31⋊C3×Dic61, … |
| maximal quotient of | C3×C31×Dic61, C31×Dic183, C5×C31×Dic61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7564, 3);