Finite Group Databasebeta

C4×Q8×C22⋊D11 #14913635

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×Q8×C22⋊D11

Splittings

FittingC22×C4×Q8×C11 ⋊ C2
SylowC11 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC22×C22⋊D11C23
hypercenterC22×C4×Q8D11
hypocenterC11C4×D4×Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

3148 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, 329430);