Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #390 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D71 |
| commutator | C22×C71 | C22×C4 |
| Fitting, prime radical | C22×D4×C71 | C2 |
| socle, cosocle | C23×C71 | C23 |
| hypercenter | C22×D4 | D71 |
| hypocenter | C71 | #390 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
258 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^6,71|a^2=f,b^2=df,c^2=e,b^a=bd,c^a=ce,g^a=g^70,g^b=g^70728 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 452);