Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C43 ⋊ #2844 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#382 | C2 |
| hypercenter | #382 | D43 |
| hypocenter | C43 | #2844 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #382 | |
356 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 133 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=ef,b^2=g,c^2=g,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^42614 conjugacy classes — view the full character table.
| maximal subgroup of | #24999667, #24999668, #24999670, … |
| maximal normal subgroup of | #24999667, #24999668, #24999670, … |
| maximal quotient of | #25027402, #25027404, #25027411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12782);