Finite Group Databasebeta

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C3×Dic3×C289 #23780805

order10404
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C3×C4×C289 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C289
unambiguous semidirect productC3⋊(C3×C4×C289)

Splittings

derivedC3 ⋊ C3×C4×C289
HallC32×C289 ⋊ C4
SylowC32 ⋊ C4×C289

Subgroups

subgroupG/H
center, hypercenterC2×C3×C289D3
commutator, hypocenterC3C3×C4×C289
FrattiniC2×C17C3×D3×C17
FittingC2×C32×C289C2
socle, prime radicalC2×C32×C17C2×C17
cosocleC2×C3×C17C2×C3×C17
LCSG ▷ C3
UCSC1 ◁ C2×C3×C289

42 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5202 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 15);