Finite Group Databasebeta

C2×#19143985 #25963317

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143985

Splittings

FittingC2×C43×B(4,𝔽2) ⋊ C2
SylowC43 ⋊ C2×#3025

Subgroups

subgroupG/H
centerC22#120×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×B(4,𝔽2)C2
socleC22×C43C2×#120
hypercenterC2×B(4,𝔽2)D43
hypocenterC43C2×#3025
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×B(4,𝔽2)

5086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036288);