Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | #405×D43 |
| Fitting | C43×#405 ⋊ C2 |
| Sylow | C43 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#405 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | #405 | D43 |
| hypocenter | C43 | C2×#405 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ #405 | |
592 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1378, D43×#1379, #25011468, … |
| maximal normal subgroup of | D43×#1378, D43×#1379, #25011468, … |
| maximal quotient of | C8×M16×D43, D43×#1450, D43×#1451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12920);