Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#13063264 |
| Fitting | C4×C16×C43 ⋊ C2 |
| Sylow | C43 ⋊ C4×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8 | C2×D43 |
| commutator | C2×C43 | C2×C4×C8 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C4×C16×C43 | C2 |
| socle | C22×C43 | C22×C8 |
| hypercenter | C4×C16 | D43 |
| hypocenter | C43 | C4×M32 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4×C8 ◁ C4×C16 | |
196 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13063264, #25005575, #25005577, … |
| maximal normal subgroup of | C8×#13063264, #25005575, #25005577, … |
| maximal quotient of | C8×#13063264, #25005589, #25005618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6101);