Finite Group Databasebeta

C2×#19135308 #25099341

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

Aliases

direct productC2×#19135308

Splittings

SylowC43 ⋊ C2×#1938

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C4×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#416D43
hypocenterC43C2×#1938
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

1074 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 172312);