C₂₉×#1770 #16815484

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1770

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 3712

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

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7168, C₂₉×#7170, C₂₉×#8202, …
maximal normal subgroup of	C₂₉×#7168, C₂₉×#7170, C₂₉×#8202, …
maximal quotient of	C₂₉×#8260, C₂₉×#8261, C₂₉×#8265, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 502);

C29×#1770 #16815484