Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C26×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2846 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C26×C43 | C2 |
| hypercenter | C26 | D43 |
| hypocenter | C43 | #2846 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C26 | |
3422 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|b^a=be,c^a=cf,d^a=dg,h^a=h^421388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #25128174, #25128176, #25129041, … |
| maximal normal subgroup of | #25128174, #25128176, #25129041, … |
| maximal quotient of | #25027753, #25027806, #25027812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12787);