C₂₉×#2889 #16816603

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#2889

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×2₋¹⁺⁴	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

704 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 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)(30,31,34,39,35,38,47,52)(32,40,42,53,43,36,46,49)(33,37,45,51,44,50,57,60)(41,54,56,61,55,48,58,59);(30,32,35,43)(31,36,38,40)(33,41,44,55)(34,46,47,42)(37,48,50,54)(39,53,52,49)(45,58,57,56)(51,61,60,59);(30,33)(31,37)(32,41)(34,45)(35,44)(36,48)(38,50)(39,51)(40,54)(42,56)(43,55)(46,58)(47,57)(49,59)(52,60)(53,61);(33,44)(37,50)(41,55)(45,57)(48,54)(51,60)(56,58)(59,61)

Conjugacy classes & character table

1189 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#13096, C₂₉×#13098, C₂₉×#21780, …
maximal normal subgroup of	C₂₉×#13096, C₂₉×#13098, C₂₉×#21780, …
maximal quotient of	C₂₉×#17351, C₂₉×#17352, C₂₉×#17368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1621);