C₄×C₉×C₂₃×C₂₉ #37562139

order	24012
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₄₀₁₂
abelian	C₄×C₉×C₂₃×C₂₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₂₃×C₂₉
socle, prime radical	C₂×C₃×C₂₃×C₂₉	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 24012

A minimal faithful permutation representation — 1 generator on 65 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)

Conjugacy classes & character table

24012 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₂₀₀₆, D₂₄₀₁₂
maximal subgroup of	Dic₁₂₀₀₆, D₂₄₀₁₂
maximal normal subgroup of	Dic₁₂₀₀₆, D₂₄₀₁₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 1);

C4×C9×C23×C29 #37562139