C₂₉×#2020 #16815734

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2020

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

342 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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)(34,35,40,45)(36,46,50,57)(37,51,55,60)(38,44,39,43)(41,49,58,48)(42,54,61,53)(47,62,64,56)(52,59,63,65);(31,33)(34,36)(35,41)(37,52)(38,49)(39,48)(40,50)(42,59)(43,57)(44,46)(45,58)(47,54)(51,62)(53,64)(55,63)(56,60)(61,65);(34,37,40,55)(35,42,45,61)(36,47,50,64)(38,54,39,53)(41,56,58,62)(43,60,44,51)(46,59,57,65)(48,52,49,63)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7399, C₂₉×#7401, C₂₉×#12111, …
maximal normal subgroup of	C₂₉×#7399, C₂₉×#7401, C₂₉×#12111, …
maximal quotient of	C₂₉×#9976, C₂₉×#9979, C₂₉×#9989, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 752);