Finite Group Databasebeta

C2×#19134971 #25098095

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19134971

Splittings

FittingC2×C43×#520 ⋊ C2
SylowC43 ⋊ C2×#1883

Subgroups

subgroupG/H
centerC23#13063294
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#520C2
socleC23×C43#120
prime radicalC22×#13063350C2
cosocleC22×C4×C43C24
hypercenterC2×#520D43
hypocenterC43C2×#1883
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#520

2018 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171066);