C₂×C₃²×C₁₃×C₆₇ #30627903

order	15678
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

abelian

C₂×C₃²×C₁₃×C₆₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 88
transitive degree	μ_t(G) = 15678

A minimal faithful permutation representation — 2 generators on 88 points:

(1,2)(3,4,5)(9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88);(6,7,8)

Conjugacy classes & character table

15678 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊Dic₂₆₁₃, C₆₇×C₃⋊Dic₃₉, C₁₃×C₃⋊Dic₂₀₁, …
socle of	C₃²×C₄×C₁₃×C₆₇, C₃⋊Dic₂₆₁₃, C₆₇×C₃⋊Dic₃₉, …
maximal subgroup of	C₃²×C₄×C₁₃×C₆₇, C₃⋊Dic₂₆₁₃, C₆₇×C₃⋊Dic₃₉, …
maximal normal subgroup of	C₃²×C₄×C₁₃×C₆₇, C₃⋊Dic₂₆₁₃, C₆₇×C₃⋊Dic₃₉, …
maximal quotient of	C₃²×C₄×C₁₃×C₆₇, C₂²×C₃²×C₁₃×C₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15678, 25);

C2×C32×C13×C67 #30627903