C₂₉×#2022 #16815736

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2022

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₂₉
prime radical	C₂₉×#534	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂⁴×C₂₉ ◁ G

430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 928

A minimal faithful permutation representation — 3 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)(30,31)(32,33)(34,35)(36,39)(37,40)(38,41)(42,45)(43,46)(44,48)(47,49);(34,36,38,43)(35,39,41,46)(37,42,44,49)(40,47,48,45);(31,33)(34,37)(35,40)(36,42)(38,44)(39,45)(41,48)(43,49)(46,47)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7395, C₂₉×#12092, C₂₉×#12094, …
maximal normal subgroup of	C₂₉×#7395, C₂₉×#12092, C₂₉×#12094, …
maximal quotient of	C₂₉×#9918, C₂₉×#9919, C₂₉×#9920, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 754);