Finite Group Databasebeta

C2×C4×Dic386 #27135724

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic386

Splittings

SylowC193 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D193
commutatorC2×C193C23×C4
FrattiniC22C23×D193
FittingC2×C42×C193C2
socle, prime radicalC23×C193C23
cosocleC22×C193C24
hypercenterC2×C42D193
hypocenterC193C2×C4×Q8
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22×C4 ◁ C2×C42

298 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, 1014);