C₂₉×#3022 #16816736

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#3022

Subgroups

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

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

normal subgroups only

This group has 704 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)(30,31,36,41)(32,42,45,54)(33,38,47,53)(34,40,35,39)(37,48,51,44)(43,57,60,56)(46,55,49,52)(50,58,61,59);(30,32)(31,37)(33,43)(34,44)(35,48)(36,45)(38,50)(39,42)(40,54)(41,51)(46,58)(47,60)(49,59)(52,56)(53,61)(55,57);(30,33)(31,38)(32,43)(34,46)(35,49)(36,47)(37,50)(39,52)(40,55)(41,53)(42,56)(44,58)(45,60)(48,59)(51,61)(54,57);(30,34,36,35)(31,39,41,40)(32,44,45,48)(33,46,47,49)(37,42,51,54)(38,52,53,55)(43,58,60,59)(50,56,61,57)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#13355, C₂₉×#13356, C₂₉×#13361, …
maximal normal subgroup of	C₂₉×#13355, C₂₉×#13356, C₂₉×#13361, …
maximal quotient of	C₂₉×#18136, C₂₉×#18140, C₂₉×#18146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1754);