C₃×C₄×C₅×C₁₇×C₂₃ #37553274

order	23460
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₃₄₆₀
abelian	C₃×C₄×C₅×C₁₇×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₅×C₁₇×C₂₃
socle, prime radical	C₂×C₃×C₅×C₁₇×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 23460

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

23460 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₁₇₃₀, D₂₃₄₆₀
maximal subgroup of	Dic₁₁₇₃₀, D₂₃₄₆₀
maximal normal subgroup of	Dic₁₁₇₃₀, D₂₃₄₆₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 1);

C3×C4×C5×C17×C23 #37553274