C₂×C₅×C₅₃×C₅₉ #44530780

order	31270
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₂₇₀
abelian	C₂×C₅×C₅₃×C₅₉
multiplicative	(ℤ/31271)ˣ, (ℤ/62542)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 31270

A minimal faithful permutation representation — 1 generator on 119 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)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119)

Conjugacy classes & character table

31270 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₆₃₅, C₂×D₁₅₆₃₅
socle of	Dic₁₅₆₃₅, C₂×D₁₅₆₃₅
maximal subgroup of	Dic₁₅₆₃₅, C₂×D₁₅₆₃₅
maximal normal subgroup of	Dic₁₅₆₃₅, C₂×D₁₅₆₃₅
automorphism group of	C₃₁₂₇₁
outer automorphism group of	C₃₁₂₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31270, 1);

C2×C5×C53×C59 #44530780