Finite Group Databasebeta

C2×#20259996 #27136379

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

Aliases

direct productC2×#20259996

Splittings

SylowC193 ⋊ C2×M32

Subgroups

subgroupG/H
centerC22C2×#13095402
commutatorC2×C193C22×C8
FrattiniC2C22×#13095402
FittingC2×C4×C193C8
socleC22×C193C2×C8
prime radicalC22×D193C8
cosocle#13095400C23
hypercenterC2×C4#13095402
hypocenterC193C2×M32
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×C4

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1669);