Finite Group Databasebeta

C2×#19133259 #25064904

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19133259

Splittings

SylowC43 ⋊ C2×#1544

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#431C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC42×C43C24
hypercenterC2×#431D43
hypocenterC43C2×#1544
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

994 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137875);