C₂₉×#3480 #16817194

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3480

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 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)(31,34)(35,37)(38,39,42,44)(40,43,41,45);(30,31)(32,35)(33,34)(36,37)(38,40,42,41)(39,43,44,45);(38,41,42,40)(39,43,44,45);(31,34)(35,37);(30,32,33,36)(31,35,34,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8437, C₂₉×#17510, C₂₉×#17515, …
maximal normal subgroup of	C₂₉×#8437, C₂₉×#17510, C₂₉×#17515, …
maximal quotient of	C₂₉×#34121, Q₈×C₂₉×#117, C₂₉×#34125, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2212);

C29×#3480 #16817194