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C2×C17×(C31⋊C3)⋊C5 #30629023

order15810
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C17×(C31⋊C3)⋊C5
unambiguous semidirect product(C2×C31⋊C3)⋊(C5×C17)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C3×C17)
unambiguous semidirect product(C2×C17×C31⋊C3)⋊C5
unambiguous semidirect product(C2×C17×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socle, HallC2×C17×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C2×C3×C5×C17
HallC2×C17×ΓL(1,𝔽32) ⋊ C3
HallC2×C17×C31⋊C3 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C2×C3
HallC17×C31⋊C3 ⋊ C2×C5
HallC17×C31 ⋊ C2×C3×C5
HallC2×ΓL(1,𝔽32) ⋊ C3×C17
HallC2×C31⋊C3 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ C2×C3×C17
HallC31⋊C3 ⋊ C2×C5×C17
HallC2×C31 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C2×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C17×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1054

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C17×(C31⋊C3)⋊C5, C17×((C31⋊C3)⋊C4)⋊C5, Dic17×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC4×C17×(C31⋊C3)⋊C5, C17×((C31⋊C3)⋊C4)⋊C5, Dic17×(C31⋊C3)⋊C5, …
maximal quotient ofC4×C17×(C31⋊C3)⋊C5, C22×C17×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 4);