C₈×C₁₉×C₃₂ #18013287

order	4864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 73728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

abelian

C₈×C₁₉×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle, prime radical	C₂²×C₁₉	C₄×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 2 generators on 59 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)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(33,34,35,36,37,38,39,40)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₈×C₁₉×C₆₄, C₁₆×C₁₉×C₃₂, C₂×C₈×C₁₉×C₃₂, …
maximal normal subgroup of	C₈×C₁₉×C₆₄, C₁₆×C₁₉×C₃₂, C₂×C₈×C₁₉×C₃₂, …
maximal quotient of	C₈×C₁₉×C₆₄, C₁₆×C₁₉×C₃₂, C₂×C₈×C₁₉×C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 316);

C8×C19×C32 #18013287