C₂₉×#2018 #16815732

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2018

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 382 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)(36,44)(37,42)(38,41)(39,43)(40,45)(46,49)(47,48);(31,33)(34,36)(35,40)(37,46)(38,45)(39,47)(41,48)(42,44)(43,49);(35,41)(36,45)(37,38)(42,43)(44,48)(46,47)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7398, C₂₉×#7400, C₂₉×#12108, …
maximal normal subgroup of	C₂₉×#7398, C₂₉×#7400, C₂₉×#12108, …
maximal quotient of	C₂₉×#9974, C₂₉×#9977, C₂₉×#9986, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 750);