C₂₉×#1885 #16815599

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#1885

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

360 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 112 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)(31,33)(34,35,38,43,39,41,37,42)(36,44,47,40,46,49,45,48);(30,31,32,33)(34,36)(35,40)(37,47)(38,45)(39,46)(41,48)(42,49)(43,44);(35,41)(37,38)(40,48)(45,47)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7487, C₂₉×#7495, C₂₉×#12761, …
maximal normal subgroup of	C₂₉×#7487, C₂₉×#7495, C₂₉×#12761, …
maximal quotient of	C₂₉×#8957, C₂₉×#8961, C₂₉×#8999, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 617);