C₂₉×#2374 #16816088

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

Aliases

direct product

C₂₉×#2374

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

552 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)(35,38)(39,41)(42,43)(44,48)(45,46)(47,49);(30,32,33,31)(43,46)(47,48);(34,35,37,38)(36,39,40,41)(42,44)(43,47)(45,49)(46,48);(34,36,37,40)(35,39,38,41)(42,43)(44,47)(45,46)(48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12959, C₂₉×#13042, C₂×C₂₉×#2374, …
maximal normal subgroup of	C₂₉×#12959, C₂₉×#13042, C₂×C₂₉×#2374, …
maximal quotient of	C₂₉×#13807, C₂₉×#13819, C₂₉×#13822, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1106);

C29×#2374 #16816088