Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Q8×C4⋊Dic43 |
| Sylow | C43 ⋊ Q8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C2×C4×Q8×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×C4×Q8 | D43 |
| hypocenter | C43 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
568 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 333 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
890 conjugacy classes — view the full character table.
| maximal subgroup of | #24990769, #24990773, #24990797, … |
| maximal normal subgroup of | #24990769, #24990773, #24990797, … |
| maximal quotient of | C4⋊C4×C4⋊Dic43, Q8×C43⋊#95, #25018143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7426);