Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C79×#2840 ⋊ C2 |
| Sylow | C79 ⋊ #36675 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D79 |
| commutator, socle, cosocle | C23×C79 | C25 |
| Fitting | C79×#2840 | C2 |
| hypercenter | #2840 | D79 |
| hypocenter | C79 | #36675 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|e^2=g,b^a=bf,c^a=cg,d^a=dh,i^a=i^78,c^b=ch,d^c=dfh,i^c=i^78,i^e=i^781066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 376001);