Finite Group Databasebeta

C2×#20259891 #27135781

order12352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20259891

Splittings

SylowC193 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D193
commutator, cosocleC22×C193C24
FrattiniC22C23×D193
FittingC2×C42×C193C2
socle, prime radicalC23×C193C23
hypercenterC2×C42D193
hypocenterC193C2×#125
LCSG ▷ C22×C193 ▷ C193
UCSC1 ◁ C23 ◁ C2×C42

226 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1071);