C₄×C₅×C₂₃×C₇₉ #49138137

order	36340
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₆₃₄₀
abelian	C₄×C₅×C₂₃×C₇₉
multiplicative	(ℤ/36341)ˣ, (ℤ/72682)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₂₃×C₇₉
socle, prime radical	C₂×C₅×C₂₃×C₇₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 111
transitive degree	μ_t(G) = 36340

A minimal faithful permutation representation — 1 generator on 111 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111)

Conjugacy classes & character table

36340 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₃₆₃₄₁
outer automorphism group of	C₃₆₃₄₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36340, 1);

C4×C5×C23×C79 #49138137