C₂₉×#1891 #16815605

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

Aliases

direct product

C₂₉×#1891

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#120
commutator	C₂³	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#386
prime radical	C₂₉×#525	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 342 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)(30,31,34,38,35,32,36,40)(33,39,42,45,41,37,43,44);(30,32,34,40,35,31,36,38)(33,39,43,44,41,37,42,45);(30,33)(31,37)(32,39)(34,43)(35,41)(36,42)(38,45)(40,44)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12755, C₂₉×#12756, C₂₉×#12757, …
maximal normal subgroup of	C₂₉×#12755, C₂₉×#12756, C₂₉×#12757, …
maximal quotient of	C₂₉×#8965, C₂₉×#8966, C₂₉×#8967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 623);