Finite Group Databasebeta

C2×#19148291 #26004646

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#19148291

Splittings

FittingC22×#123×C43 ⋊ C2
SylowC43 ⋊ C2×#3491

Subgroups

subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC22×#123×C43C2
socleC23×C43C25
prime radicalC2×#14583458C2
hypercenterC22×#123D43
hypocenterC43C2×#3491
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#123

7390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1077617);