Finite Group DatabasebetaFinite Group Databasebeta| order | 7362 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D409 |
| Fitting, socle, Hall | C32×C409 ⋊ C2 |
| derived, Sylow | C409 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D409 |
| commutator, hypocenter | C409 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C409 | C2 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
1854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#13109888, C3×C3⋊#13109888, C3×D3×D409, … |
| maximal normal subgroup of | C32×#13109888, C3×C3⋊#13109888, C3×D3×D409, … |
| maximal quotient of | C32×Dic409, C2×C32×D409, C32×C5×D409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7362, 12);