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C₂²×C₉×D₇ #92637

order	504
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₉×D₇

Splittings

Fitting	C₂²×C₇×C₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂³×C₉
Hall	C₇×C₉ ⋊ C₂³

Subgroups

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2)(3,4)(6,7)(8,9)(10,11)(12,16,20,14,19,15,17,13,18);(3,4)(5,6,8,10,11,9,7);(1,2)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₂×D₇)⋊Dic₉, C₉×(C₂×D₇)⋊C₄, C₂×D₇×Dic₉, …
maximal normal subgroup of	(C₂×D₇)⋊Dic₉, C₉×(C₂×D₇)⋊C₄, C₂×D₇×Dic₉, …
maximal quotient of	C₂×C₉×Dic₁₄, C₂×C₄×C₉×D₇, C₂×C₉×D₂₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 63);