Finite Group Databasebeta

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C3×C5×D3×C289 #39907199

order26010
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C289 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D3×C289
unambiguous semidirect productC3⋊(C2×C3×C5×C289)

Splittings

Fitting, HallC32×C5×C289 ⋊ C2
derivedC3 ⋊ C2×C3×C5×C289
HallC32×C289 ⋊ C2×C5
HallC32×C5 ⋊ C2×C289
SylowC32 ⋊ C2×C5×C289

Subgroups

subgroupG/H
center, hypercenterC3×C5×C289D3
commutator, hypocenterC3C2×C3×C5×C289
FrattiniC17C3×C5×D3×C17
FittingC32×C5×C289C2
socleC32×C5×C17C2×C17
prime radicalC3×C5×D3×C17C17
cosocleC3×C17C2×C3×C5×C17
LCSG ▷ C3
UCSC1 ◁ C3×C5×C289

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8670

Conjugacy classes & character table

13005 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26010, 13);