Finite Group Databasebeta

C2×C4×#13063251 #25094310

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#13063251

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C2×C4×#104

Subgroups

subgroupG/H
centerC2×C42C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C4×M16×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C2×C4×#104
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×M16

1878 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167281);