Finite Group Databasebeta

C8×Dic386 #27135384

order12352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic386

Splittings

SylowC193 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D193
commutatorC2×C193C22×C8
FrattiniC2×C4C22×D193
FittingC4×C8×C193C2
socle, prime radicalC22×C193C22×C4
cosocleC2×C4×C193C23
hypercenterC4×C8D193
hypocenterC193C8×Q8
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C8 ◁ C4×C8

102 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, 674);