C₂₉×#1376 #16815090

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1376

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₉	D₄
commutator	C₄	C₄×C₈×C₂₉
Frattini, cosocle	C₂²×C₈	C₂²×C₂₉
socle	C₂²×C₂₉	C₄⋊C₈
prime radical	C₂³×C₂₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 2 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)(32,33)(34,35,37,42,38,41,45,48,39,43,46,49,36,40,44,47);(31,33)(35,40,43,41)(42,47,49,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7107, C₂₉×#7108, C₂₉×#7114, …
maximal normal subgroup of	C₂₉×#7107, C₂₉×#7108, C₂₉×#7114, …
maximal quotient of	C₂₉×#7138, C₂₉×#7143, C₂₉×#7146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 108);

C29×#1376 #16815090