C₂₉×#2005 #16815719

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

Aliases

direct product

C₂₉×#2005

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

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

normal subgroups only

This group has 362 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)(37,41)(38,47)(39,43)(40,45)(42,48)(46,49);(34,36,39,37)(35,40,43,49)(38,46,48,45)(41,47,44,42);(31,33)(34,37,39,36)(35,41,43,44)(38,45,48,46)(40,42,49,47)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2005, C₂₉×#23399, C₂₉×#23401, …
maximal normal subgroup of	C₂×C₂₉×#2005, C₂₉×#23399, C₂₉×#23401, …
maximal quotient of	C₂₉×#9917, C₂₉×#9919, C₂₉×#9925, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 737);