C₂²×C₁₉×C₆₄ #18019694

order	4864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₁₉×C₆₄
multiplicative	(ℤ/9736)ˣ, (ℤ/14604)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃₂	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 87 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)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(65,66);(67,68)

Conjugacy classes & character table

4864 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₁₉×C₁₂₈, C₂³×C₁₉×C₆₄, C₂×C₄×C₁₉×C₆₄, …
maximal normal subgroup of	C₂²×C₁₉×C₁₂₈, C₂³×C₁₉×C₆₄, C₂×C₄×C₁₉×C₆₄, …
maximal quotient of	C₂²×C₁₉×C₁₂₈, C₂³×C₁₉×C₆₄, C₂×C₄×C₁₉×C₆₄, …
automorphism group of	C₈×C₁₂₁₇
outer automorphism group of	C₈×C₁₂₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6723);

C22×C19×C64 #18019694