Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic211 |
| derived, Sylow | C211 ⋊ C32×C4 |
| Hall | C32×C211 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D211 |
| commutator, hypocenter | C211 | C32×C4 |
| Frattini | C2 | C32×D211 |
| Fitting, socle | C2×C32×C211 | C2 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C2×C32 | |
36 conjugacy classes of subgroups.
1926 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic211⋊C5, C32×Dic1055, C32×C5×Dic211, … |
| maximal normal subgroup of | C32×Dic211⋊C5, C32×C5×Dic211 |
| maximal quotient of | C32×Dic1055, C32×C5×Dic211, C32×C211⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 21);