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C3×D4485 #41002129

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

Aliases

direct productC3×D4485
unambiguous semidirect productC3⋊(C3×D1495)
unambiguous semidirect productC5⋊(C3×D897)
unambiguous semidirect productC23⋊(C3×D195)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derivedC3×C5×C13×C23 ⋊ C2×C3
HallC32×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ C3×D3
HallC32×C5×C23 ⋊ D13
HallC32×C5×C13 ⋊ D23
HallC13×C23 ⋊ C3×D15
HallC32×C23 ⋊ D65
HallC32×C13 ⋊ D115
HallC5×C23 ⋊ C3×D39
HallC5×C13 ⋊ C3×D69
HallC32×C5 ⋊ D299
SylowC23 ⋊ C3×D195
SylowC13 ⋊ C3×D345
SylowC32 ⋊ D1495
SylowC5 ⋊ C3×D897

Subgroups

subgroupG/H
center, hypercenterC3D4485
commutator, cosocle, hypocenterC3×C5×C13×C23C2×C3
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C3×C5×C13×C23
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8970

Conjugacy classes & character table

6732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 56);