Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#13063370 |
| Fitting | C23×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C2×C43 | C26 |
| Frattini | C2 | C25×D43 |
| Fitting | C23×D4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C23×D4 | D43 |
| hypocenter | C43 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
908 conjugacy classes — view the full character table.
| maximal subgroup of | #25095730, #25095731, #25095733, … |
| maximal normal subgroup of | #25095730, #25095731, #25095733, … |
| maximal quotient of | C22×#14583371, C22×#14583372, C22×#14583374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 19311);