Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C79 ⋊ #14320 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator | C23×C79 | C23×C4 |
| Fitting | C79×#1442 | C2 |
| socle, prime radical, cosocle | C24×C79 | C24 |
| hypercenter | #1442 | D79 |
| hypocenter | C79 | #14320 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ #1442 | |
1318 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20224 |
Polycyclic presentation:
2^8,79|a^2=h,b^2=e,c^2=ef,d^2=efh,b^a=be,c^a=cf,i^a=i^78,c^b=cg,i^b=i^78,d^c=de,i^c=i^78,i^d=i^781780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 96570);