C₂₉×#1398 #16815112

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₉×#1398

Subgroups

	subgroup	G/H
center	C₈×C₂₉	C₄²
commutator	C₄	C₄×C₈×C₂₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₉
socle	C₂×C₂₉	#346
prime radical	C₂²×C₂₉	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 2 generators on 61 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)(30,31,32,37,33,39,42,52,34,40,43,50,44,54,56,60,35,38,41,51,45,53,55,61,46,36,47,48,57,49,58,59);(31,36,38,40)(32,41)(37,50,51,48)(39,49,53,54)(42,55)(43,47)(52,60,61,59)(56,58)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7333, C₂₉×#7389, C₂₉×#7390, …
maximal normal subgroup of	C₂₉×#7333, C₂₉×#7389, C₂₉×#7390, …
maximal quotient of	C₂₉×#7330, C₂₉×#7332, C₂₉×#7466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 130);

C29×#1398 #16815112