Finite Group Databasebeta

C2×#20259855 #27135712

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20259855

Splittings

SylowC193 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D193
commutatorC2×C193C23×C4
FrattiniC22C23×D193
FittingC2×C22⋊C4×C193C2
socleC23×C193C23
prime radicalC24×C193C22
cosocleC22×C193C24
hypercenterC2×C22⋊C4D193
hypocenterC193C2×#117
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1002);