C₂₉×#2360 #16816074

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2360

Subgroups

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

620 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)(31,33)(34,35,37,36)(38,39)(40,41)(42,43)(44,45);(34,36,37,35)(39,43)(41,44);(30,31)(32,33)(38,40)(39,44)(41,43)(42,45);(38,41,42,44)(39,40,43,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#22854, C₂₉×#22859, C₂₉×#22862, …
maximal normal subgroup of	C₂₉×#22854, C₂₉×#22859, C₂₉×#22862, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₂₉, C₂₉×#13814, C₂₉×#13817, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1092);

C29×#2360 #16816074