Finite Group Databasebeta

C2×#19145201 #25966374

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

Aliases

direct productC2×#19145201

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C2×#3172

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×M16×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC2×C4×M16D43
hypocenterC43C2×#3172
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

1986 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, 1039345);