C₁₉⋊C₃×C₇₉ #17985161

order	4503
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉⋊C₃×C₇₉
unambiguous semidirect product	C₁₉⋊(C₃×C₇₉)

Splittings

Fitting, socle, Hall	C₁₉×C₇₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₃×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₇₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₇₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₇₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 98
transitive degree	μ_t(G) = 1501

A minimal faithful permutation representation — 2 generators on 98 points:

(2,3,5)(4,7,8)(6,10,9)(11,15,13)(12,16,14)(17,19,18)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98);(1,2,4,8,13,18,15,3,6,11,16,5,9,14,7,12,17,19,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₉×#4296, #27214009, #27214010, …
maximal normal subgroup of	C₇₉×#4296, #27214009, #27214010, …
maximal quotient of	C₇₉×#4294, C₃×C₁₉⋊C₃×C₇₉, C₇₉×C₂²⋊(C₁₉⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4503, 1);

C19⋊C3×C79 #17985161