Finite Group Databasebeta

← Prev (#22604932) Next (#22604934) →

C₂²×C₃₁×C₅²⋊C₃ #22604933

order	9300
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₃₁ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₃₁×C₅²⋊C₃

Splittings

Fitting, socle, Hall	C₂²×C₅²×C₃₁ ⋊ C₃
derived, Sylow	C₅² ⋊ C₂²×C₃×C₃₁
Hall	C₅²×C₃₁ ⋊ C₂²×C₃
Hall	C₂²×C₅² ⋊ C₃×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃₁	C₅²⋊C₃
commutator, hypocenter	C₅²	C₂²×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₃₁	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²×C₃₁

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	A₄×C₃₁×C₅²⋊C₃, C₅²⋊C₃×C₂²⋊(C₃₁⋊C₃), C₂²×C₅²⋊C₃×C₃₁⋊C₃, …
maximal normal subgroup of	A₄×C₃₁×C₅²⋊C₃, C₅²⋊C₃×C₂²⋊(C₃₁⋊C₃), C₂²×C₅²⋊C₃×C₃₁⋊C₃, …
maximal quotient of	C₂²×C₃₁×C₅²⋊C₉, C₂×D₃×C₃₁×C₅²⋊C₃, C₂²×C₃×C₃₁×C₅²⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 207);