Finite Group Databasebeta

C2×#19134565 #25095932

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19134565

Splittings

SylowC43 ⋊ C2×#1795

Subgroups

subgroupG/H
centerC22#14582755
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC22×H(5,𝔽2)×C43C2
socleC22×C43#379
cosocleC22×C4×C43C24
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C2×#1795
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×H(5,𝔽2)

3946 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1486 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168903);