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C₂²×C₁₃×C₁₃⋊C₉ #20258807

order	6084
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₃×C₁₃⋊C₉

Splittings

derived	C₁₃ ⋊ C₂²×C₉×C₁₃
Hall	C₂²×C₁₃² ⋊ C₉
Sylow	C₁₃² ⋊ C₂²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₁₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₁₃
Frattini	C₃	C₂²×C₁₃×C₁₃⋊C₃
Fitting, socle	C₂²×C₃×C₁₃²	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃×C₁₃

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₅×C₁₃×C₁₃⋊C₉, C₂²×C₅×C₁₃×C₁₃⋊C₉
maximal normal subgroup of	C₂²×C₅×C₁₃×C₁₃⋊C₉
maximal quotient of	C₂×D₅×C₁₃×C₁₃⋊C₉, C₂²×C₅×C₁₃×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6084, 114);