Finite Group Databasebeta

C2×#19135131 #25098594

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135131

Splittings

FittingC2×C43×H(3,ℤ/4) ⋊ C2
SylowC43 ⋊ C2×#1912

Subgroups

subgroupG/H
centerC22#14582777
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43C2×#1912
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

1694 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171565);