Finite Group Databasebeta

C2×#20259856 #27135713

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20259856

Splittings

FittingC2×C42×C193 ⋊ C2
SylowC193 ⋊ C2×#117

Subgroups

subgroupG/H
centerC22×C4C2×D193
commutatorC2×C193C23×C4
FrattiniC22C23×D193
FittingC2×C42×C193C2
socleC23×C193C23
prime radicalC23×D193C22
cosocleC22×C193C24
hypercenterC2×C42D193
hypocenterC193C2×#117
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22×C4 ◁ C2×C42

330 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, 1003);