C₂₉×#3495 #16817209

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3495

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

1022 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)(32,36)(34,37)(38,39,43,46)(40,41,48,44)(42,50,51,45)(47,52,53,49);(30,31,33,35)(32,34,36,37)(38,40,43,48)(39,44,46,41)(42,47,51,53)(45,52,50,49);(30,32)(31,34)(33,36)(35,37)(38,41)(39,40)(42,49)(43,44)(45,47)(46,48)(50,53)(51,52);(38,40)(39,41)(42,47)(43,48)(44,46)(45,49)(50,52)(51,53);(38,42,43,51)(39,45,46,50)(40,47,48,53)(41,49,44,52)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8468, C₂₉×#17605, C₂₉×#17609, …
maximal normal subgroup of	C₂₉×#8468, C₂₉×#17605, C₂₉×#17609, …
maximal quotient of	C₂₉×#34180, C₂₉×#34202, C₂₉×#34203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2227);

C29×#3495 #16817209