Finite Group Databasebeta

C2×Q8×C11⋊C16 #14907255

order2816
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×C11⋊C16

Splittings

SylowC11 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C8C22×D11
commutatorC2×C11C23×C16
FrattiniC2×C8C23×D11
FittingC2×C8×Q8×C11C2
socle, prime radicalC23×C11C22×C8
cosocleC2×C8×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11C2×Q8×C16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 323050);