C₂₉×#1375 #16815089

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1375

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₄²
commutator	C₄	C₄×C₈×C₂₉
Frattini, cosocle	C₂²×C₈	C₂²×C₂₉
socle	C₂²×C₂₉	#97
prime radical	C₂³×C₂₉	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

140 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)(34,35,37,42,38,40,46,47,39,43,45,49,36,41,44,48);(31,33)(35,40,43,41)(37,45)(42,48,49,47)(44,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7109, C₂₉×#7116, C₂₉×#7117, …
maximal normal subgroup of	C₂₉×#7109, C₂₉×#7116, C₂₉×#7117, …
maximal quotient of	C₂₉×#7137, C₂₉×#7142, C₂₉×#7145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 107);

C29×#1375 #16815089