C₄×C₁₇×C₆₄ #16865253

order	4352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian

C₄×C₁₇×C₆₄

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₇
socle, prime radical	C₂²×C₁₇	C₂×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 2 generators on 85 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);(65,66,67,68)

Conjugacy classes & character table

4352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₁₇×C₁₂₈, C₈×C₁₇×C₆₄, C₂×C₄×C₁₇×C₆₄, …
maximal normal subgroup of	C₄×C₁₇×C₁₂₈, C₈×C₁₇×C₆₄, C₂×C₄×C₁₇×C₆₄, …
maximal quotient of	C₄×C₁₇×C₁₂₈, C₈×C₁₇×C₆₄, C₂×C₄×C₁₇×C₆₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 497);

C4×C17×C64 #16865253