C₁₉×D₆₇ #14579296

order	2546
isoclinism	isoclinic class of D₆₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₆₇
unambiguous semidirect product	C₆₇⋊(C₂×C₁₉)

Splittings

Fitting, socle, Hall	C₁₉×C₆₇ ⋊ C₂
derived, Sylow	C₆₇ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₆₇
commutator, cosocle, hypocenter	C₆₇	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₆₇	C₂
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 86
transitive degree	μ_t(G) = 1273

A minimal faithful permutation representation — 2 generators on 86 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₁₉×D₆₇, C₁₉×D₃₃₅, C₇×C₁₉×D₆₇, …
maximal normal subgroup of	C₅×C₁₉×D₆₇, C₇×C₁₉×D₆₇, C₁₁×C₁₉×D₆₇, …
maximal quotient of	C₅×C₁₉×D₆₇, C₁₉×D₃₃₅, C₇×C₁₉×D₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2546, 2);

C19×D67 #14579296