C₂⁴×C₄²×C₆₁ #29566071

order	15616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

abelian

C₂⁴×C₄²×C₆₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁶×C₆₁
socle, prime radical	C₂⁶×C₆₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

24030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 15616

A minimal faithful permutation representation — 6 generators on 77 points:

(1,2,3,4)(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);(5,6,7,8);(9,10);(11,12);(13,14);(15,16)

Conjugacy classes & character table

15616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₄×C₈×C₆₁, C₂³×C₄³×C₆₁, C₂⁵×C₄²×C₆₁
maximal normal subgroup of	C₂⁴×C₄×C₈×C₆₁, C₂³×C₄³×C₆₁, C₂⁵×C₄²×C₆₁
maximal quotient of	C₂⁴×C₄×C₈×C₆₁, C₂³×C₄³×C₆₁, C₂⁵×C₄²×C₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 55626);

C24×C42×C61 #29566071