Finite Group DatabasebetaFinite Group Databasebeta| order | 7088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D443 |
| unambiguous semidirect product | C23⋊D443 |
| Fitting | C23×C443 ⋊ C2 |
| Sylow | C443 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D443 |
| commutator | C2×C443 | C23 |
| Frattini | C2 | C22×D443 |
| Fitting | C23×C443 | C2 |
| socle | C22×C443 | C22 |
| hypercenter | C23 | D443 |
| hypocenter | C443 | C2×D4 |
| LCS | G ▷ C2×C443 ▷ C443 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
1778 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28381800, (C22⋊D443)⋊C4, C4×C22⋊D443, … |
| maximal normal subgroup of | #28381800, (C22⋊D443)⋊C4, C4×C22⋊D443, … |
| maximal quotient of | C2×(C2×D443)⋊C4, C2×C22⋊Dic443, C2×Dic443⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7088, 35);