Finite Group Databasebeta

C3×C23×Dic6 #13110247

order1656
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic6
unambiguous semidirect productC3⋊(C3×Q8×C23)

Splittings

HallC32×C23 ⋊ Q8
SylowC32 ⋊ Q8×C23

Subgroups

subgroupG/H
centerC2×C3×C23C2×D3
commutator, cosocleC2×C3C22×C3×C23
FrattiniC2C2×C3×D3×C23
FittingC32×C4×C23C2
socle, prime radicalC2×C32×C23C22
hypercenterC3×C4×C23D3
hypocenterC3C3×Q8×C23
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C23 ◁ C3×C4×C23

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 552

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1656, 85);