C₂₉×#3515 #16817229

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

Aliases

direct product

C₂₉×#3515

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
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) = 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)(31,34)(35,37)(38,39,43,44)(40,41,45,48)(42,50,51,46)(47,53,52,49);(39,44)(41,48)(46,50)(49,53);(30,31)(32,35)(33,34)(36,37)(38,40,43,45)(39,41,44,48)(42,47,51,52)(46,49,50,53);(38,41)(39,45)(40,44)(42,49)(43,48)(46,52)(47,50)(51,53);(30,32,33,36)(31,35,34,37)(38,42)(39,46)(40,47)(41,49)(43,51)(44,50)(45,52)(48,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8415, C₂₉×#17653, C₂₉×#17680, …
maximal normal subgroup of	C₂₉×#8415, C₂₉×#17653, C₂₉×#17680, …
maximal quotient of	C₂₉×#34191, C₂₉×#34229, C₂₉×#34231, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2247);

C29×#3515 #16817229