C₂×C₅×C₇×C₉×C₃₇ #37551982

order	23310
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₃₃₁₀
abelian	C₂×C₅×C₇×C₉×C₃₇
multiplicative	(ℤ/23311)ˣ, (ℤ/46622)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅×C₇×C₃₇
socle, prime radical	C₂×C₃×C₅×C₇×C₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 23310

A minimal faithful permutation representation — 1 generator on 60 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)

Conjugacy classes & character table

23310 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₂₃₃₁₁
outer automorphism group of	C₂₃₃₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 1);

C2×C5×C7×C9×C37 #37551982