Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Sylow | C79 ⋊ #63076 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C25×D79 |
| commutator, socle | C2×C79 | C25×C4 |
| Fitting, prime radical | C2×#585×C79 | C2 |
| cosocle | C4×C79 | C26 |
| hypercenter | C2×#585 | D79 |
| hypocenter | C79 | #63076 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ C2×#585 | |
10796 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|a^2=g,g^2=h,f^a=fh,i^a=i^78,e^b=eh,d^c=dh2782 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1083340);