Finite Group Databasebeta

C2×#20259820 #27135246

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

Aliases

direct productC2×#20259820

Splittings

SylowC193 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D193
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
Fitting, prime radicalC22×D4×C193C2
socleC23×C193D4
cosocleC2×C4×C193C23
hypercenterC22×D4D193
hypocenterC193C2×#102
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 536);