Finite Group Databasebeta

C2×#20259840 #27135679

order12352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20259840

Splittings

FittingC2×D8×C193 ⋊ C2
SylowC193 ⋊ C2×D16

Subgroups

subgroupG/H
centerC22#15690540
commutator, cosocleC8×C193C23
FrattiniC8C22×D193
FittingC2×D8×C193C2
socleC22×C193D8
hypercenterC2×D8D193
hypocenterC193C2×D16
LCSG ▷ C8×C193 ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 969);