Finite Group Databasebeta

C2×#322×D43 #25062164

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#322×D43

Splittings

FittingC2×C43×#322 ⋊ C2
SylowC43 ⋊ C22×#322

Subgroups

subgroupG/H
centerC2×C42C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC42C23×D43
FittingC2×C43×#322C2
socleC23×C43C2×C42
prime radicalC23×D43C42
cosocleC42×C43C24
hypercenterC2×#322D43
hypocenterC43C22×#322
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C2×#322

1182 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135135);