Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#10621885 |
| Sylow | C43 ⋊ C23×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22⋊D43 |
| commutator | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C23×Q8×C43 | C2 |
| socle | C24×C43 | D4 |
| hypercenter | C23×Q8 | D43 |
| hypocenter | C43 | C23×Q16 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×Q8 | |
1464 conjugacy classes of subgroups.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #25003405, #25003406, #25003432, … |
| maximal normal subgroup of | #25003405, #25003406, #25003432, … |
| maximal quotient of | C23×#13063248, C23×#13063249, C23×#13063258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19232);