Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #443×D43 |
| Fitting | C43×#443 ⋊ C2 |
| Sylow | C43 ⋊ C2×#443 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D43 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#443 | C2 |
| socle | C2×C43 | C2×C4×D4 |
| hypercenter | #443 | D43 |
| hypocenter | C43 | C2×#443 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #443 | |
472 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1335, #25006382, D43×#1336, … |
| maximal normal subgroup of | D43×#1335, #25006382, D43×#1336, … |
| maximal quotient of | C8×D8×D43, C8×SD16×D43, C8×Q16×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13396);