Finite Group Databasebeta

C2×#19135125 #25098587

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

Aliases

direct productC2×#19135125

Splittings

FittingC22×#100×C43 ⋊ C2
SylowC43 ⋊ C2×#1911

Subgroups

subgroupG/H
centerC22#14582776
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#100×C43C2
socleC22×C43#386
prime radicalC2×#14583466C2
cosocleC22×C4×C43C24
hypercenterC22×#100D43
hypocenterC43C2×#1911
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1974 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, 171558);