Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C71 ⋊ C2 |
| Sylow | C71 ⋊ #518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D71 |
| commutator | C2×C71 | C23×C4 |
| Fitting | #117×C71 | C2 |
| socle, cosocle | C22×C71 | C24 |
| prime radical | C22×D284 | C2 |
| hypercenter | #117 | D71 |
| hypocenter | C71 | #518 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^6,71|a^2=f,b^a=be,d^a=de,c^b=ce,g^b=g^70,g^c=g^70734 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 1023);