Finite Group Databasebeta

C2×Dic6×C41 #14520238

order1968
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C41 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic6×C41
unambiguous semidirect product(C2×C3)⋊(Q8×C41)

Splittings

HallC3×C41 ⋊ C2×Q8
SylowC3 ⋊ C2×Q8×C41

Subgroups

subgroupG/H
centerC22×C41C2×D3
commutator, cosocleC2×C3C23×C41
FrattiniC2C22×D3×C41
FittingC2×C3×C4×C41C2
socle, prime radicalC22×C3×C41C22
hypercenterC2×C4×C41D3
hypocenterC3C2×Q8×C41
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C41 ◁ C2×C4×C41

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1968

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 161);