C₂₉×#2171 #16815885

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×#2171

Subgroups

	subgroup	G/H
center	C₈×C₂₉	C₂×D₄
commutator	C₄	C₂²×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂×C₂₉	C₈×D₄
prime radical	C₂₉×#135	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

144 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12068, C₂₉×#12465, C₂₉×#12466, …
maximal normal subgroup of	C₂₉×#12068, C₂₉×#12465, C₂₉×#12466, …
maximal quotient of	C₂₉×#12038, C₂₉×#12049, C₂₉×#12050, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 903);