Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C4×#13063293 |
| Fitting | C2×C4×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C4×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×C4×D4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×D4 | D43 |
| hypocenter | C43 | C4×#120 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
1224 conjugacy classes of subgroups.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #24991280, #24991282, #24991290, … |
| maximal normal subgroup of | #24991280, #24991282, #24991290, … |
| maximal quotient of | C4×#14582775, C4×#14582779, C4×#14582770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7010);