Finite Group DatabasebetaFinite Group Databasebeta| order | 7088 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic443 |
| unambiguous semidirect product | C443⋊C42 |
| derived, Sylow | C443 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D443 |
| commutator, hypocenter | C443 | C42 |
| Frattini | C22 | C2×D443 |
| Fitting | C2×C4×C443 | C2 |
| socle | C22×C443 | C22 |
| LCS | G ▷ C443 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
1784 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic443, #28381796, #28381812, … |
| maximal normal subgroup of | C8×Dic443, #28381796, #28381812, … |
| maximal quotient of | C443⋊#95, C8×Dic443, C4×C443⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7088, 16);