C₂²×C₃×C₁₉×C₇₁ #30633686

order	16188
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₁₉×C₇₁
multiplicative	(ℤ/18893)ˣ, (ℤ/24291)ˣ, (ℤ/37786)ˣ, (ℤ/48582)ˣ

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 16188

A minimal faithful permutation representation — 2 generators on 97 points:

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

Conjugacy classes & character table

16188 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₁₉×C₇₁, C₂³×C₃×C₁₉×C₇₁
maximal normal subgroup of	C₂×C₃×C₄×C₁₉×C₇₁, C₂³×C₃×C₁₉×C₇₁
maximal quotient of	C₂×C₃×C₄×C₁₉×C₇₁, C₂³×C₃×C₁₉×C₇₁
automorphism group of	C₇×C₂₆₉₉
outer automorphism group of	C₇×C₂₆₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16188, 13);

C22×C3×C19×C71 #30633686