C₂₉×#2818 #16816532

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₂₉×#2818

Subgroups

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

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

normal subgroups only

This group has 630 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) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#18462, C₂₉×#18464, C₂×C₂₉×#2818, …
maximal normal subgroup of	C₂₉×#18462, C₂₉×#18464, C₂×C₂₉×#2818, …
maximal quotient of	C₂₉×#14623, C₂₉×#14624, C₂₉×#14661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1550);