Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2858 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C2×C4⋊Q8×C43 | C2 |
| hypercenter | C2×C4⋊Q8 | D43 |
| hypocenter | C43 | #2858 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^42,h^b=h^42,h^d=h^42632 conjugacy classes — view the full character table.
| maximal subgroup of | #24995646, #24995656, #24995661, … |
| maximal normal subgroup of | #24995646, #24995656, #24995661, … |
| maximal quotient of | #25027788, #25027866, #25027939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12868);