Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#10621902 |
| Fitting | Q82×C43 ⋊ C2 |
| Sylow | C43 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator, socle | C22×C43 | C25 |
| Fitting | Q82×C43 | C2 |
| hypercenter | Q82 | D43 |
| hypocenter | C43 | Q8×#41 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
575 conjugacy classes — view the full character table.
| maximal subgroup of | #25072572, #25072580, #25072587, … |
| maximal normal subgroup of | #25072572, #25072580, #25072587, … |
| maximal quotient of | C4⋊C4×#10621902, Q8×#13063283, #25256253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 18093);