Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×Dic43⋊C4 |
| Sylow | C43 ⋊ C2×C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C23 | C23×D43 |
| Fitting | C22×C42×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | C2×C4×C4⋊C4 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
928 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#14582624, #24987112, #24989255, … |
| maximal normal subgroup of | C4×#14582624, #24987112, #24989255, … |
| maximal quotient of | C2×C4×C43⋊#95, C42×Dic43⋊C4, C2×#19132821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6846);