C₂₉×#2352 #16816066

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#2352

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(32,33)(34,35,36,37)(39,40)(43,44);(31,33)(38,39,42,40)(41,44,45,43);(38,40,42,39)(41,44,45,43);(30,31)(32,33)(38,41)(39,43)(40,44)(42,45)

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#22414, C₂₉×#22416, C₂₉×#22420, …
maximal normal subgroup of	C₂₉×#22414, C₂₉×#22416, C₂₉×#22420, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₂₉, C₂₉×#13801, C₂₉×#13804, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1084);

C29×#2352 #16816066