C₇²×C₉×C₄₃ #34038909

order	18963
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

abelian

C₇²×C₉×C₄₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₇²×C₄₃
socle, prime radical	C₃×C₇²×C₄₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 18963

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16)(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);(17,18,19,20,21,22,23)

Conjugacy classes & character table

18963 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₇⋊D₂₇₀₉
Fitting subgroup of	C₇⋊D₂₇₀₉, C₄₃×C₇⋊D₆₃, C₇×D₂₇₀₉, …
maximal subgroup of	C₂×C₇²×C₉×C₄₃, C₇⋊D₂₇₀₉, C₄₃×C₇⋊D₆₃, …
maximal normal subgroup of	C₂×C₇²×C₉×C₄₃, C₇⋊D₂₇₀₉, C₄₃×C₇⋊D₆₃, …
maximal quotient of	C₂×C₇²×C₉×C₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18963, 16);

C72×C9×C43 #34038909