Finite Group Databasebeta

Q8×(C2×D11)⋊C8 #14770286

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×(C2×D11)⋊C8

Splittings

FittingC2×C8×Q8×C11 ⋊ C2
SylowC11 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC2×C8×Q8×C11C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11Q8×C22⋊C8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 186081);