Finite Group Databasebeta

C2×#20259821 #27135247

order12352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20259821

Splittings

FittingC22×C8×C193 ⋊ C2
SylowC193 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23D772
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
FittingC22×C8×C193C2
socleC23×C193D4
prime radicalC22×D772C2
cosocleC2×C4×C193C23
hypercenterC22×C8D193
hypocenterC193C2×#102
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

202 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, 537);