C₂₉×#3461 #16817175

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

Aliases

direct product

C₂₉×#3461

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
prime radical	C₂₉×#537	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8321, C₂₉×#8402, C₂₉×#17469, …
maximal normal subgroup of	C₂₉×#8321, C₂₉×#8402, C₂₉×#17469, …
maximal quotient of	C₂₉×#34059, C₂₉×#34060, C₂₉×#34083, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2193);

C29×#3461 #16817175