Finite Group Databasebeta

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C5×Dic3×C289 #31773192

order17340
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C289 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C289
unambiguous semidirect productC3⋊(C4×C5×C289)

Splittings

derived, SylowC3 ⋊ C4×C5×C289
HallC3×C5×C289 ⋊ C4
HallC3×C289 ⋊ C4×C5
HallC3×C5 ⋊ C4×C289

Subgroups

subgroupG/H
center, hypercenterC2×C5×C289D3
commutator, hypocenterC3C4×C5×C289
FrattiniC2×C17C5×D3×C17
FittingC2×C3×C5×C289C2
socle, prime radicalC2×C3×C5×C17C2×C17
cosocleC2×C3×C17C2×C5×C17
LCSG ▷ C3
UCSC1 ◁ C2×C5×C289

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17340

Conjugacy classes & character table

8670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17340, 5);