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C3×D2485 #28415850

order14910
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D2485
unambiguous semidirect productC5⋊(C3×D497)
unambiguous semidirect productC71⋊(C3×D35)

Splittings

Fitting, socle, HallC3×C5×C7×C71 ⋊ C2
derived, HallC5×C7×C71 ⋊ C2×C3
HallC3×C7×C71 ⋊ D5
HallC3×C5×C71 ⋊ D7
HallC7×C71 ⋊ C3×D5
HallC5×C71 ⋊ C3×D7
HallC3×C71 ⋊ D35
HallC3×C5×C7 ⋊ D71
SylowC71 ⋊ C3×D35
HallC5×C7 ⋊ C3×D71
HallC3×C7 ⋊ D355
HallC3×C5 ⋊ D497
SylowC7 ⋊ C3×D355
SylowC5 ⋊ C3×D497

Subgroups

subgroupG/H
center, hypercenterC3D2485
commutator, cosocle, hypocenterC5×C7×C71C2×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C71C2
LCSG ▷ C5×C7×C71
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7455

Conjugacy classes & character table

3732 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D35×D71, C3×D7×D355, C3×D5×D497, …
maximal normal subgroup ofC3×D35×D71, C3×D7×D355, C3×D5×D497, …
maximal quotient ofC3×Dic2485, C2×C3×D2485

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 13);