Finite Group Databasebeta

C2×#20259839 #27135674

order12352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20259839

Splittings

SylowC193 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D193
commutatorC2×C193C22×C8
FrattiniC8C22×D193
FittingC22×C8×C193C2
socleC22×C193C2×C8
prime radicalC23×C193C8
cosocleC8×C193C23
hypercenterC22×C8D193
hypocenterC193C2×M32
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 964);