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C2×C3×(C31⋊C3)⋊C5 #14584063

order2790
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C31⋊C3)⋊C5
unambiguous semidirect product(C2×C31⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C2×C3×C31⋊C3)⋊C5
unambiguous semidirect product(C2×C3×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC2×C3×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C2×C32×C5
HallC2×C3×C31⋊C3 ⋊ C5
HallC2×ΓL(1,𝔽32) ⋊ C32
HallC3×C31⋊C3 ⋊ C2×C5
HallΓL(1,𝔽32) ⋊ C2×C32
HallC2×C31 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 186

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×(C31⋊C3)⋊C5, C2×C3×C5×(C31⋊C3)⋊C5, AGL(1,𝔽7)×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC2×C3×C5×(C31⋊C3)⋊C5, C2×C3×C7×(C31⋊C3)⋊C5, C2×C3×C11×(C31⋊C3)⋊C5, …
maximal quotient ofC2×C3×(C31⋊C3)⋊C25, C3×D5×(C31⋊C3)⋊C5, C2×C3×C5×(C31⋊C3)⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2790, 23);