Finite Group Databasebeta

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C3×C5×D897 #41002125

order26910
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D897
unambiguous semidirect productC3⋊(C3×C5×D299)
unambiguous semidirect productC23⋊(C3×C5×D39)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derivedC3×C13×C23 ⋊ C2×C3×C5
HallC32×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ C3×D3
HallC32×C5×C23 ⋊ D13
HallC32×C5×C13 ⋊ D23
HallC13×C23 ⋊ C3×C5×D3
HallC32×C23 ⋊ C5×D13
HallC32×C13 ⋊ C5×D23
HallC5×C23 ⋊ C3×D39
HallC5×C13 ⋊ C3×D69
HallC32×C5 ⋊ D299
SylowC23 ⋊ C3×C5×D39
SylowC13 ⋊ C3×C5×D69
SylowC32 ⋊ C5×D299

Subgroups

subgroupG/H
center, hypercenterC3×C5D897
commutator, cosocle, hypocenterC3×C13×C23C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C3×C13×C23
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8970

Conjugacy classes & character table

6750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 52);