Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×M128 ⋊ C2 |
| Sylow | C11 ⋊ #13737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C22×D11 |
| commutator, socle | C2×C11 | C22×C32 |
| Fitting | C11×M128 | C2 |
| prime radical | #4339 | C16 |
| cosocle | C11×C32 | C23 |
| hypercenter | M128 | D11 |
| hypocenter | C11 | #13737 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C32 ◁ M128 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^10,c^b=ch,i^c=i^10560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 90608);