Finite Group Databasebeta

C2×#20259816 #27135236

order12352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20259816

Splittings

SylowC193 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic193
commutatorC22×C193C22×C4
FrattiniC2×C4C22×D193
Fitting, prime radicalC22×D4×C193C2
socleC22×C193C22⋊C4
cosocleC2×C4×C193C23
hypercenterC22×D4D193
hypocenterC193C2×#100
LCSG ▷ C22×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1942 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 526);