Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#401 ⋊ C4 |
| Sylow | C53 ⋊ #14620 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6157 |
| commutator, socle | C23×C53 | C23×C4 |
| Fitting | C53×#401 | C4 |
| prime radical, cosocle | C23×D53 | C24 |
| hypercenter | #401 | #6157 |
| hypocenter | C53 | #14620 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #401 | |
1094 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 1094 conjugacy classes of subgroups — too many to draw. Only its 226 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=h,b^2=ef,c^2=egh,d^2=fg,b^a=be,c^a=cf,d^a=def,i^a=i^23,c^b=cg,d^b=de,i^c=i^30,i^h=i^52350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1099115);