Finite Group Databasebeta

C2×Q16×C43⋊C8 #25065968

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q16×C43⋊C8

Splittings

SylowC43 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC2×C4×Q16×C43C2
socle, prime radicalC23×C43C4×D4
cosocleC42×C43C24
hypercenterC2×C4×Q16D43
hypocenterC43C2×C8×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

734 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138939);