Finite Group Databasebeta

C2×#354×D43 #25249370

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

Aliases

direct productC2×#354×D43

Splittings

FittingC2×C43×#354 ⋊ C2
SylowC43 ⋊ C22×#354

Subgroups

subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C23×C4
FrattiniC2×D4C23×D43
FittingC2×C43×#354C2
socleC22×C43C2×#99
prime radicalC22×D4×D43C22
cosocleC2×D4×C43C24
hypercenterC2×#354D43
hypocenterC43C22×#354
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

1502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322341);