Finite Group Databasebeta

C2×#19144725 #25964800

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19144725

Splittings

SylowC43 ⋊ C2×#3113

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×C4×Q8×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC22×C4×Q8D43
hypocenterC43C2×#3113
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

2118 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, 1037771);