Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#10621885 |
| Sylow | C43 ⋊ C8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22⋊D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C42 | C22×D43 |
| Fitting | C8×Q8×C43 | C2 |
| socle | C22×C43 | C4×D4 |
| hypercenter | C8×Q8 | D43 |
| hypocenter | C43 | C8×Q16 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q8 | |
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
896 conjugacy classes — view the full character table.
| maximal subgroup of | #25008388, C16×#10621885, #25008393, … |
| maximal normal subgroup of | #25008388, C16×#10621885, #25008393, … |
| maximal quotient of | C8×#13063249, C8×#13063248, C8×#13063258, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 3315);