C₂₉×#3531 #16817245

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 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 — 5 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)(32,38)(33,37)(34,36)(35,39)(40,44)(41,43)(42,45)(46,47)(48,51)(49,56)(50,53)(52,58)(54,61)(55,60)(57,59);(30,32)(31,35)(33,40)(34,39)(36,38)(37,42)(41,45)(43,44)(46,48,50,55)(47,51,53,60)(49,57,58,54)(52,61,56,59);(32,39)(35,38)(40,45)(42,44)(46,49,50,58)(47,52,53,56)(48,54,55,57)(51,59,60,61);(31,36)(32,39)(37,43)(40,45)(47,53)(51,60)(52,56)(59,61);(30,33,34,41)(31,37,36,43)(32,40,39,45)(35,42,38,44)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8505, C₂₉×#18990, C₂₉×#18991, …
maximal normal subgroup of	C₂₉×#8505, C₂₉×#18990, C₂₉×#18991, …
maximal quotient of	C₂₉×#34348, C₂₉×#34350, C₄×C₂₉×#562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2263);