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C17×(C31⋊C3)⋊C5 #21463636

order7905
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C5×C17)
unambiguous semidirect productΓL(1,𝔽32)⋊(C3×C17)
unambiguous semidirect product(C17×C31⋊C3)⋊C5
unambiguous semidirect product(C17×ΓL(1,𝔽32))⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC17(C31⋊C3)⋊C5
commutator, hypocenterC31C3×C5×C17
FrattiniC1G
Fitting, socleC17×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C17

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

289 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C17×(C31⋊C3)⋊C5, C17×AGL(1,𝔽31), D17×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC2×C17×(C31⋊C3)⋊C5, C17×AGL(1,𝔽31), D17×(C31⋊C3)⋊C5, …
maximal quotient ofC2×C17×(C31⋊C3)⋊C5, C17×ΓL(1,𝔽32)⋊C9, C3×C17×(C31⋊C3)⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7905, 4);