C₂₉×#2153 #16815867

order	3712
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2153

Subgroups

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

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(30,31,34,39,35,38,48,53,36,40,49,54,33,46,47,59)(32,41,44,56,45,51,58,60,42,55,57,61,43,37,50,52);(30,32,33,43,36,42,35,45)(31,37,38,41,40,51,46,55)(34,44,47,50,49,57,48,58)(39,52,53,56,54,60,59,61);(32,42)(37,51)(41,55)(43,45)(44,57)(50,58)(52,60)(56,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#11989, C₂₉×#11990, C₂₉×#11991, …
maximal normal subgroup of	C₂₉×#11989, C₂₉×#11990, C₂₉×#11991, …
maximal quotient of	C₂₉×#11997, C₂₉×#12005, C₂₉×#12014, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 885);

C29×#2153 #16815867