C₂₉×#1287 #16815001

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₉×#1287

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#95
commutator	C₂×C₄	C₄²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂²×C₂₉
prime radical	C₂³×C₂₉	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 1856

A minimal faithful permutation representation — 2 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)(30,31,33,38,35,39,34,37)(32,40,41,36,43,44,42,45)(46,47)(48,54,56,60)(49,52)(50,53)(51,55,58,61)(57,59);(30,32,34,42,35,43,33,41)(31,36,38,44,39,45,37,40)(46,48)(47,51,53,58)(49,55)(50,56)(52,54,59,60)(57,61)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1287, C₂₉×#7964, C₂₉×#7965, …
maximal normal subgroup of	C₂×C₂₉×#1287, C₂₉×#7964, C₂₉×#7965, …
maximal quotient of	C₂₉×#7018, C₂₉×#7021, C₂₉×#7023, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 19);