Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#393×C79 ⋊ C2 |
| Sylow | C79 ⋊ #14717 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator, socle, cosocle | C24×C79 | C24 |
| Fitting | C2×#393×C79 | C2 |
| prime radical | C25×D79 | C22 |
| hypercenter | C2×#393 | D79 |
| hypocenter | C79 | #14717 |
| LCS | G ▷ C24×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ C2×#393 | |
3654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=e,b^2=e,b^a=be,c^a=cf,d^a=dh,c^b=cg,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, 100956);