Finite Group Databasebeta

C2×#19143143 #25960197

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143143

Splittings

FittingC2×C4×#41×C43 ⋊ C2
SylowC43 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC2×C4C22×D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×#41×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583735C2
cosocleC2×C4×C43C25
hypercenterC2×C4×#41D43
hypocenterC43C2×#2901
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×#41 ◁ C2×C4×#41

4946 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033168);