C₂₉×#3538 #16817252

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3538

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
prime radical	C₂₉×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

1014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 53 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)(31,34)(32,36)(38,39,43,45)(40,46,48,41)(42,50,51,44)(47,49,53,52);(31,34)(35,37)(38,40,43,48)(39,41,45,46)(42,47,51,53)(44,49,50,52);(30,31)(32,35)(33,34)(36,37);(30,32)(31,35)(33,36)(34,37)(38,41)(39,40)(42,49)(43,46)(44,47)(45,48)(50,53)(51,52);(38,42,43,51)(39,44,45,50)(40,47,48,53)(41,49,46,52)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8482, C₂₉×#12757, C₂₉×#18230, …
maximal normal subgroup of	C₂₉×#8482, C₂₉×#12757, C₂₉×#18230, …
maximal quotient of	C₂₉×#34360, C₂₉×#34380, C₂₉×#34412, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2270);

C29×#3538 #16817252