C₃×C₄×C₅×C₁₁×C₃₇ #37567480

order	24420
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₄₄₂₀
abelian	C₃×C₄×C₅×C₁₁×C₃₇
multiplicative	(ℤ/24421)ˣ, (ℤ/48842)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃×C₅×C₁₁×C₃₇
socle, prime radical	C₂×C₃×C₅×C₁₁×C₃₇	C₂
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) = 24420

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

24420 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₂₁₀, D₂₄₄₂₀
maximal subgroup of	Dic₁₂₂₁₀, D₂₄₄₂₀
maximal normal subgroup of	Dic₁₂₂₁₀, D₂₄₄₂₀
automorphism group of	C₂₄₄₂₁
outer automorphism group of	C₂₄₄₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 1);

C3×C4×C5×C11×C37 #37567480