Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C43×#390 ⋊ C2 |
| Sylow | C43 ⋊ #2375 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#390 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | #2375 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=g,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^d=h^42626 conjugacy classes — view the full character table.
| maximal subgroup of | #25013363, #25013367, #25013870, … |
| maximal normal subgroup of | #25013363, #25013367, #25013870, … |
| maximal quotient of | #25018214, #25018225, #25018226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 7647);