C₁₉×C₇₉⋊C₃ #17985162

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

Aliases

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

Splittings

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

Subgroups

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

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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉⋊C₃×C₇₉⋊C₃, C₃×C₁₉×C₇₉⋊C₃, C₁₉×C₂²⋊(C₇₉⋊C₃), …
maximal normal subgroup of	C₁₉⋊C₃×C₇₉⋊C₃, C₃×C₁₉×C₇₉⋊C₃, C₅×C₁₉×C₇₉⋊C₃, …
maximal quotient of	C₁₉×C₇₉⋊C₉, C₃×C₁₉×C₇₉⋊C₃, C₁₉×C₂²⋊(C₇₉⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4503, 2);

C19×C79⋊C3 #17985162