Finite Group Databasebeta

C8×#66945 #14751975

order2816
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#66945

Splittings

FittingC8×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ C8×#117

Subgroups

subgroupG/H
centerC22×C8C22×D11
commutatorC2×C11C22×C4×C8
FrattiniC22×C4C23×D11
FittingC8×C11×C4⋊C4C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenterC8×C4⋊C4D11
hypocenterC11C8×#117
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 167770);