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C₃×Dic₃×D₇ #92666

order	504
isoclinism	isoclinic class of D₃×D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₃×Dic₃×D₇

Splittings

derived	C₃×C₇ ⋊ C₂×C₃×C₄
Hall	C₃²×C₇ ⋊ C₂×C₄
Sylow	C₃² ⋊ C₄×D₇
Sylow	C₇ ⋊ C₂×C₃×Dic₃

Subgroups

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 84

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

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×Dic₃×D₇, D₇×#624, D₇×#626, …
maximal normal subgroup of	D₃×Dic₃×D₇, D₇×#624, D₇×#626, …
maximal quotient of	C₃×D₇×C₃⋊C₈, C₃×#66557, C₃×Dic₃×Dic₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 92);