C₂₉×#2947 #16816661

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2947

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#117 ◁ G

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 49 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)(30,31,33,32)(35,39)(37,44)(40,46)(41,45)(43,48)(47,49);(34,35,38,41)(36,40,42,47)(37,45,44,39)(43,49,48,46);(30,32,33,31)(34,36)(35,40)(37,43)(38,42)(39,46)(41,47)(44,48)(45,49);(36,42)(40,47)(43,48)(46,49)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#22890, C₂₉×#22892, C₂₉×#22894, …
maximal normal subgroup of	C₂₉×#22890, C₂₉×#22892, C₂₉×#22894, …
maximal quotient of	C₂₉×#17853, C₂₉×#17874, C₂₉×#17876, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1679);

C29×#2947 #16816661