Finite Group Databasebeta

C2×#20259906 #27136022

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20259906

Splittings

SylowC193 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D193
commutatorC2×C193C23×C4
FrattiniC4C23×D193
Fitting, prime radicalC2×#41×C193C2
socleC22×C193C22×C4
cosocleC4×C193C24
hypercenterC2×#41D193
hypocenterC193C2×#131
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1312);