C₂₉×#2295 #16816009

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

Aliases

direct product

C₂₉×#2295

Subgroups

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

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7562, C₂₉×#7577, C₂₉×#7581, …
maximal normal subgroup of	C₂₉×#7562, C₂₉×#7577, C₂₉×#7581, …
maximal quotient of	C₂₉×#13755, C₂₉×#13759, C₄×C₂₉×#387, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1027);

C29×#2295 #16816009