C₂₉×#2158 #16815872

order	3712
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#2158

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	D₈
commutator	C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂²×C₂₉	C₂×D₈
prime radical	C₂³×C₂₉	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 65 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)(36,45)(37,42)(38,52)(39,54)(40,44)(41,48)(43,46)(47,58)(49,64)(50,60)(51,57)(53,65)(55,62)(56,63)(59,61);(34,36,46,61,39,49,53,63,40,50,51,62,37,47,38,48)(35,41,52,58,42,55,57,60,44,56,65,64,54,59,43,45);(34,37,40,39)(35,42,44,54)(36,47,50,49)(38,51,53,46)(41,55,56,59)(43,52,57,65)(45,58,60,64)(48,62,63,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7473, C₂₉×#7475, C₂₉×#7477, …
maximal normal subgroup of	C₂₉×#7473, C₂₉×#7475, C₂₉×#7477, …
maximal quotient of	C₂₉×#12008, C₂₉×#12024, C₂₉×#12034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 890);

C29×#2158 #16815872