C₂₉×#1903 #16815617

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1902
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#1903

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#386
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×C₂₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

324 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 45
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 3 generators on 45 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)(30,31,36,39)(32,35,38,34)(33,40)(37,41)(42,44)(43,45);(30,32,34,31,36,38,35,39)(33,40,42,37,43,45,41,44);(30,33)(31,37)(32,40)(34,42)(35,41)(36,43)(38,45)(39,44)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1903, C₂₉×#20995, C₂₉×#22284, …
maximal normal subgroup of	C₂×C₂₉×#1903, C₂₉×#20995, C₂₉×#22284, …
maximal quotient of	C₂₉×#9089, C₂₉×#9090, C₂₉×#9093, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 635);