C₃×D₇×C₄₇ #14520322

order	1974
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×D₇×C₄₇

Splittings

Fitting, socle, Hall	C₃×C₇×C₄₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃×C₄₇
Hall	C₇×C₄₇ ⋊ C₂×C₃
Hall	C₃×C₇ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₇	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₄₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₄₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 987

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(5,10)(6,9)(7,8)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₇×D₄₇, D₃×D₇×C₄₇, D₇×D₁₄₁, …
maximal normal subgroup of	C₃×D₇×D₄₇, D₃×D₇×C₄₇, D₇×D₁₄₁, …
maximal quotient of	C₃×Dic₇×C₄₇, C₂×C₃×D₇×C₄₇, C₃×C₄₇×D₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1974, 6);

C3×D7×C47 #14520322