Finite Group Databasebeta

C2×#19136407 #25249719

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19136407

Splittings

SylowC43 ⋊ C2×#2165

Subgroups

subgroupG/H
centerC2×C4#13063284
commutatorC2×C4×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C4×M16×C43C2
socleC22×C43#432
prime radicalC24×C43M16
cosocleC2×C8×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C2×#2165
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ C2×C4×M16

570 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322690);