C₂₉×#3020 #16816734

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

Aliases

direct product

C₂₉×#3020

Subgroups

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

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

normal subgroups only

This group has 698 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)(32,40)(33,37)(34,46)(35,38)(36,42)(39,49)(41,57)(43,54)(44,55)(45,52)(47,51)(48,53)(50,58)(56,59)(60,61);(30,32)(31,36)(33,41)(34,47)(35,43)(37,50)(38,51)(39,54)(40,46)(42,49)(44,60)(45,59)(48,58)(52,61)(53,56)(55,57);(30,33,35,45)(31,37,38,52)(32,41,43,59)(34,48,49,44)(36,50,51,61)(39,55,46,53)(40,56,54,57)(42,60,47,58);(31,38)(36,51)(37,52)(39,46)(40,54)(50,61)(53,55)(56,57)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#23874, C₂₉×#23875, C₂₉×#23893, …
maximal normal subgroup of	C₂₉×#23874, C₂₉×#23875, C₂₉×#23893, …
maximal quotient of	C₂₉×#18134, C₂₉×#18139, C₂₉×#18142, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1752);