C₁₇×C₇₉⋊C₃ #16860916

order	4029
isoclinism	isoclinic class of C₇₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₇₉⋊C₃
unambiguous semidirect product	C₇₉⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₇×C₇₉)⋊C₃

Splittings

Fitting, socle, Hall	C₁₇×C₇₉ ⋊ C₃
derived, Sylow	C₇₉ ⋊ C₃×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	C₇₉⋊C₃
commutator, cosocle, hypocenter	C₇₉	C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₇₉	C₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₁₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 1343

A minimal faithful permutation representation — 2 generators on 96 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20,22)(21,24,29)(23,27,26)(25,31,39)(28,34,36)(30,37,33)(32,41,52)(35,44,49)(38,47,46)(40,50,43)(42,54,67)(45,57,65)(48,60,62)(51,63,59)(53,55,56)(58,70,80)(61,73,78)(64,76,75)(66,71,72)(68,81,69)(74,82,89)(77,85,87)(79,83,84)(86,90,94)(88,91,92)(93,95,96);(18,19,21,25,32,42,55,39,49,62,75,84,70,41,53,66,79,88,93,95,85,60,34,20,23,28,35,45,58,71,50,29,36,46,59,72,54,68,67,80,89,94,96,90,73,44,24,30,38,48,61,74,83,63,37,22,26,33,43,56,69,81,52,65,78,87,92,82,57,31,40,51,64,77,86,91,76,47,27)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₇×C₇₉⋊C₃, C₁₇×C₂²⋊(C₇₉⋊C₃), C₅×C₁₇×C₇₉⋊C₃, …
maximal normal subgroup of	C₃×C₁₇×C₇₉⋊C₃, C₅×C₁₇×C₇₉⋊C₃, C₇×C₁₇×C₇₉⋊C₃
maximal quotient of	C₁₇×C₇₉⋊C₉, C₃×C₁₇×C₇₉⋊C₃, C₁₇×C₂²⋊(C₇₉⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4029, 1);

C17×C79⋊C3 #16860916