Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | C2×#14582677 |
| Sylow | C43 ⋊ C2×#347 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C2×#97×C43 | C2 |
| socle | C22×C43 | #97 |
| hypercenter | C2×#97 | D43 |
| hypocenter | C43 | C2×#347 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 | |
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
884 conjugacy classes — view the full character table.
| maximal subgroup of | #24983764, #24983765, #24983766, … |
| maximal normal subgroup of | #24983764, #24983765, #24983766, … |
| maximal quotient of | C2×#19132516, #25005598, #25005639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 6112);