Finite Group DatabasebetaFinite Group Databasebeta| order | 7328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic458 |
| Sylow | C229 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D229 |
| commutator | C2×C229 | C24 |
| Frattini | C2 | C23×D229 |
| Fitting | C22×C4×C229 | C2 |
| socle | C23×C229 | C22 |
| hypercenter | C22×C4 | D229 |
| hypocenter | C229 | C22×Q8 |
| LCS | G ▷ C2×C229 ▷ C229 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
156 conjugacy classes of subgroups.
1844 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28411385, #28411386, #28411387, … |
| maximal normal subgroup of | #28411385, #28411386, #28411387, … |
| maximal quotient of | C22×#16814645, C22×C4⋊Dic229, C2×C4×Dic458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7328, 186);