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C2×C3×C5⋊(D97⋊C3) #31775559

order17460
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5⋊(D97⋊C3)
unambiguous semidirect product(C2×C5)⋊(C3×D97⋊C3)
unambiguous semidirect product(C2×C97⋊C3)⋊(C3×D5)
unambiguous semidirect product(C2×D485)⋊C32
unambiguous semidirect product(C2×C3×D485)⋊C3

Splittings

Fitting, socleC2×C3×C5×C97 ⋊ C2×C3
derived, HallC5×C97 ⋊ C22×C32
HallC3×C5×C97⋊C3 ⋊ C22
HallC2×D485 ⋊ C32
HallC3×C97⋊C3 ⋊ C2×D5
SylowC97 ⋊ C2×C32×D5
SylowC5 ⋊ C2×C3×D97⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D97⋊C3)
commutator, cosocle, hypocenterC5×C97C22×C32
FrattiniC1G
Fitting, socleC2×C3×C5×C97C2×C3
LCSG ▷ C5×C97
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 95);