Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#14583735 |
| Fitting | C22×#41×C43 ⋊ C2 |
| Sylow | C43 ⋊ C2×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D43 |
| commutator | C2×C43 | C26 |
| Frattini | C2 | C25×D43 |
| Fitting | C22×#41×C43 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | C22×#41 | D43 |
| hypocenter | C43 | C2×#585 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
5956 conjugacy classes of subgroups.
908 conjugacy classes — view the full character table.
| maximal subgroup of | #25095848, #25095849, #25095850, … |
| maximal normal subgroup of | #25095848, #25095849, #25095850, … |
| maximal quotient of | C2×#19147794, C2×#19147796, C2×#19147798, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19318);