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C23×(C31⋊C3)⋊C5 #24924122

order10695
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C5×C23)
unambiguous semidirect productΓL(1,𝔽32)⋊(C3×C23)
unambiguous semidirect product(C23×C31⋊C3)⋊C5
unambiguous semidirect product(C23×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socle, HallC23×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C3×C5×C23
HallC23×ΓL(1,𝔽32) ⋊ C3
HallC23×C31⋊C3 ⋊ C5
HallΓL(1,𝔽32) ⋊ C3×C23
HallC31⋊C3 ⋊ C5×C23

Subgroups

subgroupG/H
center, hypercenterC23(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C3×C5×C23
FrattiniC1G
Fitting, socleC23×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C23

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C23×(C31⋊C3)⋊C5, C23×AGL(1,𝔽31), D23×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC2×C23×(C31⋊C3)⋊C5, C23×AGL(1,𝔽31), D23×(C31⋊C3)⋊C5, …
maximal quotient ofC2×C23×(C31⋊C3)⋊C5, C23×ΓL(1,𝔽32)⋊C9, C3×C23×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10695, 4);