Finite Group Databasebeta

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C3×C5×Dic289 #31773189

order17340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic289

Splittings

derived, SylowC289 ⋊ C3×C4×C5
HallC3×C5×C289 ⋊ C4
HallC5×C289 ⋊ C3×C4
HallC3×C289 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D289
commutator, hypocenterC289C3×C4×C5
FrattiniC2×C17C3×C5×D17
FittingC2×C3×C5×C289C2
socle, prime radicalC2×C3×C5×C17D17
cosocleC2×C289C2×C3×C5
LCSG ▷ C289
UCSC1 ◁ C2×C3×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17340

Conjugacy classes & character table

4380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17340, 2);