Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×#10621885 |
| Sylow | C43 ⋊ Q8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | Q82×C43 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | Q82 | D43 |
| hypocenter | C43 | Q8×Q16 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 ◁ Q82 | |
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #25086747, #25086750, #25086755, … |
| maximal normal subgroup of | #25086747, #25086750, #25086755, … |
| maximal quotient of | Q8×#13063248, Q8×#13063249, C4⋊C4×#10621885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17392);