C₂×C₉×C₂₃×C₄₁ #30684055

order	16974
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₉₇₄
abelian	C₂×C₉×C₂₃×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₂₃×C₄₁
socle, prime radical	C₂×C₃×C₂₃×C₄₁	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 16974

A minimal faithful permutation representation — 1 generator on 75 points:

(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34)(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)

Conjugacy classes & character table

16974 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₉×C₂₃×Dic₄₁, C₉×C₄₁×Dic₂₃, C₉×Dic₉₄₃, …
maximal subgroup of	C₄×C₉×C₂₃×C₄₁, C₉×C₂₃×Dic₄₁, C₉×C₄₁×Dic₂₃, …
maximal normal subgroup of	C₄×C₉×C₂₃×C₄₁, C₉×C₂₃×Dic₄₁, C₉×C₄₁×Dic₂₃, …
maximal quotient of	C₄×C₉×C₂₃×C₄₁, C₂²×C₉×C₂₃×C₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16974, 1);

C2×C9×C23×C41 #30684055