Finite Group Databasebeta

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C2×C5×C3⋊(D97⋊C3) #31775561

order17460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C3⋊(D97⋊C3)
unambiguous semidirect product(C2×C3)⋊(C5×D97⋊C3)
unambiguous semidirect product(C2×C97⋊C3)⋊(C5×D3)
unambiguous semidirect product(C2×D291)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D291)⋊C3

Splittings

Fitting, socleC2×C3×C5×C97 ⋊ C2×C3
derivedC3×C97 ⋊ C22×C3×C5
HallC3×C5×C97⋊C3 ⋊ C22
HallC3×C97⋊C3 ⋊ C22×C5
HallC5×C97 ⋊ C2×C3×D3
SylowC97 ⋊ C2×C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D97⋊C3)
commutator, cosocle, hypocenterC3×C97C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C97C2×C3
LCSG ▷ C3×C97
UCSC1 ◁ C2×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 97);