C₂₉×#3039 #16816753

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#3039

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

480 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 208 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)(31,33)(34,35,39,43)(36,44,46,49)(37,42,38,41)(40,47,48,45);(30,31,32,33);(34,36)(35,40)(37,45)(38,47)(39,46)(41,44)(42,49)(43,48);(34,37,39,38)(35,41,43,42)(36,45,46,47)(40,44,48,49)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#9171, C₂₉×#9172, C₂₉×#9316, …
maximal normal subgroup of	C₂₉×#9171, C₂₉×#9172, C₂₉×#9316, …
maximal quotient of	C₂₉×#19270, C₂₉×#19271, C₂₉×#19272, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1771);