Finite Group Databasebeta

C2×#19134701 #25096450

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19134701

Splittings

SylowC43 ⋊ C2×#1828

Subgroups

subgroupG/H
centerC22#14582760
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC22×#99×C43C2
socleC22×C43#381
prime radicalC23×D4×C43C22
cosocleC24×C43C24
hypercenterC22×#99D43
hypocenterC43C2×#1828
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

1554 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 169421);