Finite Group Databasebeta

C2×#19144385 #25964100

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19144385

Splittings

FittingC22×C4⋊C8×C43 ⋊ C2
SylowC43 ⋊ C2×#3076

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×C4⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC22×C4⋊C8D43
hypocenterC43C2×#3076
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4⋊C8

2162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1037071);