Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C79×#3458 ⋊ C2 |
| Sylow | C79 ⋊ #62686 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Frattini | C22 | C25×D79 |
| Fitting | C79×#3458 | C2 |
| hypercenter | #3458 | D79 |
| hypocenter | C79 | #62686 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ #3458 | |
7226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dh,i^a=i^78,c^b=ch,i^b=i^78,i^f=i^781804 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1076432);