Finite Group Databasebeta

C2×#19132812 #25017646

order11008
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#19132812

Splittings

SylowC43 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22#14582734
commutator, cosocleC32×C43C23
FrattiniC32C22×D43
FittingC2×C43×Q64C2
socle, prime radicalC22×C43D32
hypercenterC2×Q64D43
hypocenterC43C2×Q128
LCSG ▷ C32×C43 ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×Q64

126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

868 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90617);