C₂₉×#1717 #16815431

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₂₉×#1717

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂₉×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

208 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 1856

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1717, C₂₉×#19613, C₂₉×#19619, …
maximal normal subgroup of	C₂×C₂₉×#1717, C₂₉×#19613, C₂₉×#19619, …
maximal quotient of	C₂₉×#8821, C₂₉×#9827, C₂₉×#9829, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 449);