Finite Group Databasebeta

D8×Dic193 #27135342

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

Aliases

direct productD8×Dic193

Splittings

SylowC193 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D193
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
Fitting, prime radicalC2×D8×C193C2
socleC22×C193C2×D4
cosocleC2×C4×C193C23
hypercenterC2×D8D193
hypocenterC193C4×D8
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 632);