C₂₉×#2004 #16815718

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2004

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂₉×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 394 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)(36,42)(37,45)(38,41)(39,43)(40,47)(44,49)(46,48);(34,36,38,44)(35,39,41,48)(37,46,47,43)(40,49,45,42);(31,33)(37,47)(39,48)(40,45)(43,46)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2004, C₂₉×#23399, C₂₉×#23401, …
maximal normal subgroup of	C₂×C₂₉×#2004, C₂₉×#23399, C₂₉×#23401, …
maximal quotient of	C₂₉×#9916, C₂₉×#9918, C₂₉×#9924, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 736);