Finite Group Databasebeta

C2×#20259806 #27135103

order12352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20259806

Splittings

SylowC193 ⋊ C2×#95

Subgroups

subgroupG/H
centerC24C2×D193
commutatorC2×C193C2×C42
FrattiniC23C22×D193
FittingC23×C4×C193C2
socle, prime radicalC24×C193C22
cosocleC23×C193C23
hypercenterC23×C4D193
hypocenterC193C2×#95
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C24 ◁ C23×C4

330 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 393);