C₂₉×#1913 #16815627

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#1913

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#386
commutator	C₂³	C₂²×C₄×C₂₉
Frattini, cosocle	C₂⁴	C₂³×C₂₉
prime radical	C₂₉×#534	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂⁴×C₂₉ ◁ G

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

normal subgroups only

This group has 380 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)(32,35,39,43)(33,40,41,36)(34,37)(38,42)(44,45);(30,32)(31,35,37,43)(33,38)(34,39)(36,42,40,45)(41,44);(30,33)(31,36)(32,38)(34,41)(35,42)(37,40)(39,44)(43,45)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12753, C₂₉×#12754, C₂₉×#12767, …
maximal normal subgroup of	C₂₉×#12753, C₂₉×#12754, C₂₉×#12767, …
maximal quotient of	C₂₉×#9107, C₂₉×#9108, C₂₉×#9109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 645);