Finite Group Databasebeta

M16×Dic193 #27135210

order12352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×Dic193

Splittings

SylowC193 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D193
commutatorC2×C193C2×C42
FittingC2×M16×C193C2
socleC22×C193C22×C4
prime radicalC23×C193C2×C4
cosocleC2×C4×C193C23
hypercenterC2×M16D193
hypocenterC193C4×M16
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C4 ◁ C2×M16

142 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, 500);