Finite Group Databasebeta

C2×#19135594 #25123382

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19135594

Splittings

FittingC2×C43×#340 ⋊ C2
SylowC43 ⋊ C2×#1999

Subgroups

subgroupG/H
centerC24D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC24×C43C2×D4
hypercenterC2×#340D43
hypocenterC43C2×#1999
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

2870 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, 196353);