Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D71 |
| commutator, socle, cosocle | C22×C71 | C24 |
| Fitting | C4×Q8×C71 | C2 |
| prime radical | #14556125 | C2 |
| hypercenter | C4×Q8 | D71 |
| hypocenter | C71 | #559 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 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=ef,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^70725 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 1284);