Finite Group Databasebeta

C2×#19132468 #24986510

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132468

Splittings

SylowC43 ⋊ C2×#1291

Subgroups

subgroupG/H
centerC23C43⋊#95
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC2×C43×#432C2
socleC23×C43#95
prime radicalC24×C43C4⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#432D43
hypocenterC43C2×#1291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

610 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, 59481);