C₃²×C₄×C₁₉×C₂₃ #30628573

order	15732
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

abelian

C₃²×C₄×C₁₉×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₁₉×C₂₃
socle, prime radical	C₂×C₃²×C₁₉×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 15732

A minimal faithful permutation representation — 2 generators on 52 points:

(1,2,3,4)(5,6,7)(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);(8,9,10)

Conjugacy classes & character table

15732 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₈×C₁₉×C₂₃, C₂×C₃²×C₄×C₁₉×C₂₃
maximal normal subgroup of	C₃²×C₈×C₁₉×C₂₃, C₂×C₃²×C₄×C₁₉×C₂₃
maximal quotient of	C₃²×C₈×C₁₉×C₂₃, C₂×C₃²×C₄×C₁₉×C₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 35);

C32×C4×C19×C23 #30628573