C₂×C₃×C₇×C₁₇×C₂₃ #30655976

order	16422
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₄₂₂
abelian	C₂×C₃×C₇×C₁₇×C₂₃

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 16422

A minimal faithful permutation representation — 1 generator on 52 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)

Conjugacy classes & character table

16422 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃×C₇×C₁₇×Dic₂₃, C₃×C₇×C₂₃×Dic₁₇, C₃×C₇×Dic₃₉₁, …
socle of	C₃×C₄×C₇×C₁₇×C₂₃, C₃×C₇×C₁₇×Dic₂₃, C₃×C₇×C₂₃×Dic₁₇, …
maximal subgroup of	C₃×C₄×C₇×C₁₇×C₂₃, C₃×C₇×C₁₇×Dic₂₃, C₃×C₇×C₂₃×Dic₁₇, …
maximal normal subgroup of	C₃×C₄×C₇×C₁₇×C₂₃, C₃×C₇×C₁₇×Dic₂₃, C₃×C₇×C₂₃×Dic₁₇, …
maximal quotient of	C₃×C₄×C₇×C₁₇×C₂₃, C₂²×C₃×C₇×C₁₇×C₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16422, 1);

C2×C3×C7×C17×C23 #30655976