C₁₉×C₆₇ #11929696

order	1273
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₉×C₁₁ (order 1188) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₇₃
abelian	C₁₉×C₆₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 1 generator 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)

Conjugacy classes & character table

1273 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1273, 1);

center of	A₄×C₁₉×C₆₇, D₇×C₁₉×C₆₇, D₉×C₁₉×C₆₇, …
derived subgroup of	D₁₂₇₃, #16838389, #16838390, …
Fitting subgroup of	D₁₉×C₆₇, C₁₉×D₆₇, D₁₂₇₃, …
socle of	D₁₉×C₆₇, C₁₉×D₆₇, D₁₂₇₃, …
maximal subgroup of	D₁₉×C₆₇, C₁₉×D₆₇, D₁₂₇₃, …
maximal normal subgroup of	D₁₉×C₆₇, C₁₉×D₆₇, D₁₂₇₃, …
maximal quotient of	C₂×C₁₉×C₆₇, C₃×C₁₉×C₆₇, C₁₁×C₁₉×C₆₇, …

C19×C67 #11929696