Finite Group Databasebeta

C2×#19135151 #25098638

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19135151

Splittings

SylowC43 ⋊ C2×#1916

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C23×C8
FrattiniC22×C4C23×D43
FittingC2×C43×#336C2
socle, prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC2×#336D43
hypocenterC43C2×#1916
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×#336

1134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171609);