C₂₉×#3458 #16817172

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

Aliases

direct product

C₂₉×#3458

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
prime radical	C₂⁴×C₂₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

996 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)(30,31,33,35)(32,36,37,34)(38,39)(40,46)(41,45)(42,44)(43,47)(48,52)(49,51)(50,53);(38,40)(39,43)(41,48)(42,47)(44,46)(45,50)(49,53)(51,52);(30,32,33,37)(31,34,35,36)(40,47)(43,46)(48,53)(50,52);(39,44)(43,46)(45,51)(50,52);(38,41,42,49)(39,45,44,51)(40,48,47,53)(43,50,46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8410, C₂₉×#11389, C₂₉×#11391, …
maximal normal subgroup of	C₂₉×#8410, C₂₉×#11389, C₂₉×#11391, …
maximal quotient of	C₂₉×#34052, C₂₉×#34074, C₄×C₂₉×#543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2190);

C29×#3458 #16817172