Finite Group Databasebeta

C22×#14583111 #25963382

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

Aliases

direct productC22×#14583111

Splittings

FittingC22×#124×C43 ⋊ C2
SylowC43 ⋊ C22×#463

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#124×C43C2
socleC24×C43C2×D4
prime radicalC23×#10621882C2
hypercenterC22×#124D43
hypocenterC43C22×#463
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

3350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036353);