Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C82×C53 ⋊ C4 |
| Sylow | C53 ⋊ #7844 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×#6157 |
| commutator, socle | C22×C53 | C43 |
| Fitting | C82×C53 | C4 |
| prime radical | C22×D53 | C2×C42 |
| cosocle | C42×D53 | C23 |
| hypercenter | C82 | #6157 |
| hypocenter | C53 | #7844 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C42 ◁ C82 | |
518 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,c^a=ch,c^b=cg,i^c=i^30,i^f=i^52944 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1085526);