Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C64×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13741 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D2528 |
| commutator, cosocle | C32×C79 | C23 |
| Frattini | C32 | C22×D79 |
| Fitting | C2×C64×C79 | C2 |
| socle | C2×C79 | C2×D32 |
| hypercenter | C2×C64 | D79 |
| hypocenter | C79 | #13741 |
| LCS | G ▷ C32×C79 ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|c^2=h,d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=de,e^a=ef,f^a=fg,g^a=gh,i^a=i^78,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^b=i^785062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90622);