C₂₉×#2817 #16816531

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2817

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 57
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 57 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)(35,38)(39,41)(42,43,47,45)(44,50,52,48)(46,49,55,53)(51,57,54,56);(31,33)(35,38)(36,40)(42,44,47,52)(43,48,45,50)(46,54,55,51)(49,57,53,56);(30,31)(32,33)(34,35)(36,39)(37,38)(40,41)(42,45,47,43)(44,48,52,50)(46,49,55,53)(51,57,54,56);(34,36)(35,39)(37,40)(38,41)(42,46,47,55)(43,49,45,53)(44,51,52,54)(48,56,50,57)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#9982, C₂₉×#9985, C₂₉×#12095, …
maximal normal subgroup of	C₂₉×#9982, C₂₉×#9985, C₂₉×#12095, …
maximal quotient of	C₂₉×#14626, C₂₉×#14627, C₂₉×#14629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1549);