C₂₉×#3028 #16816742

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#3028

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂₉×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

716 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 212 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)(30,31,35,39)(32,36,42,49)(33,37,44,51)(34,45,46,38)(40,52,54,47)(41,55,56,48)(43,57,58,50)(53,59,61,60);(30,32)(31,36)(33,40)(34,41)(35,42)(37,47)(38,48)(39,49)(43,53)(44,54)(45,55)(46,56)(50,59)(51,52)(57,60)(58,61);(30,33)(31,37)(32,40)(34,43)(35,44)(36,47)(38,50)(39,51)(41,53)(42,54)(45,57)(46,58)(48,59)(49,52)(55,60)(56,61);(30,34,35,46)(31,38,39,45)(32,41,42,56)(33,43,44,58)(36,48,49,55)(37,50,51,57)(40,53,54,61)(47,59,52,60)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#13351, C₂₉×#13352, C₂₉×#13354, …
maximal normal subgroup of	C₂₉×#13351, C₂₉×#13352, C₂₉×#13354, …
maximal quotient of	C₂₉×#18308, C₂₉×#18309, C₂₉×#18310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1760);