Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C2×#97×D43 |
| Fitting | C2×#97×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C2×#97×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C2×#97 | D43 |
| hypocenter | C43 | C22×#97 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
920 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1275, #24986017, D43×#1281, … |
| maximal normal subgroup of | D43×#1275, #24986017, D43×#1281, … |
| maximal quotient of | C2×#322×D43, D43×#1451, C2×#19132881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12912);