C₂₉×#2019 #16815733

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

Aliases

direct product

C₂₉×#2019

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×C₂₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 362 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) = 49
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 3 generators on 49 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)(34,35,38,42)(36,43,46,48)(37,40,47,41)(39,44,49,45);(31,33)(34,36)(35,39)(37,44)(38,46)(40,43)(41,48)(42,49)(45,47);(35,40)(36,44)(37,47)(41,42)(43,48)(45,46)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2019, C₂₉×#23438, C₂₉×#23439, …
maximal normal subgroup of	C₂×C₂₉×#2019, C₂₉×#23438, C₂₉×#23439, …
maximal quotient of	C₂₉×#9975, C₂₉×#9978, C₂₉×#9987, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 751);