Finite Group Databasebeta

C22×#14583734 #26010489

order11008
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×#14583734

Splittings

FittingC22×H(5,𝔽2)×C43 ⋊ C2
SylowC43 ⋊ C22×#585

Subgroups

subgroupG/H
centerC23C24×D43
commutator, cosocleC2×C43C27
FrattiniC2C26×D43
FittingC22×H(5,𝔽2)×C43C2
socleC23×C43C25
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C22×#585
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

60366 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083460);