Finite Group Databasebeta

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C₃²×C₂²⋊D₇ #92706

order	504
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃²×C₂²⋊D₇

Splittings

Fitting	C₂²×C₃²×C₇ ⋊ C₂
Hall	C₃²×C₇ ⋊ D₄
Sylow	C₇ ⋊ C₃²×D₄

Subgroups

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#66683, C₃×#66684, C₃×D₃×C₂²⋊D₇, …
maximal normal subgroup of	C₃×#66683, C₃×#66684, C₃×D₃×C₂²⋊D₇, …
maximal quotient of	C₃²×Dic₇⋊C₄, C₃²×(C₂×D₇)⋊C₄, C₃²×#1141, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 132);