Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#14582837 |
| Sylow | C43 ⋊ C2×#400 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C23×C43 | C24 |
| Frattini | C23 | C23×D43 |
| Fitting | C22×C4⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C4⋊C4 | D43 |
| hypocenter | C43 | C2×#400 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
604 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #24991628, #24991633, #24996839, … |
| maximal normal subgroup of | #24991628, #24991633, #24996839, … |
| maximal quotient of | C2×#19132845, C2×#19132853, C2×#19132854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7761);