Finite Group Databasebeta

C22×#14583174 #25963984

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14583174

Splittings

SylowC43 ⋊ C22×#473

Subgroups

subgroupG/H
centerC23#13063299
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#131×C43C2
socleC23×C43#121
prime radicalC22×#41×C43C22
hypercenterC22×#131D43
hypocenterC43C22×#473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#131

2630 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036955);