Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C64×D43 |
| Fitting | C43×C64 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D43 |
| commutator, hypocenter | C43 | C2×C64 |
| Frattini | C32 | C2×D43 |
| Fitting | C43×C64 | C2 |
| socle | C2×C43 | C2×C32 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×C128, #24984507, C2×C64×D43, … |
| maximal normal subgroup of | D43×C128, #24984507, C2×C64×D43, … |
| maximal quotient of | C64×Dic43, (C2×D43)⋊C64, Dic43⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2718);