Finite Group Databasebeta

C2×#20259833 #27135293

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

Aliases

direct productC2×#20259833

Splittings

SylowC193 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23D772
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
FittingC22×C8×C193C2
socle, prime radicalC23×C193D4
cosocleC2×C4×C193C23
hypercenterC22×C8D193
hypocenterC193C2×#107
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 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, 583);