Finite Group Databasebeta

C2×#20259835 #27135305

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

Aliases

direct productC2×#20259835

Splittings

SylowC193 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D772
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
FittingC22×C8×C193C2
socleC22×C193C4⋊C4
prime radicalC23×C193Q8
cosocleC2×C4×C193C23
hypercenterC22×C8D193
hypocenterC193C2×#108
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 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, 595);