C₂₉×#1882 #16815596

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

Aliases

direct product

C₂₉×#1882

Subgroups

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

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

normal subgroups only

This group has 334 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)(34,35,38,42,39,43,37,41)(36,44,46,40,47,48,45,49);(30,31,32,33)(34,36)(35,40)(37,46)(38,45)(39,47)(41,48)(42,44)(43,49);(34,36)(35,40)(37,45)(38,46)(39,47)(41,44)(42,48)(43,49)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1882, C₂₉×#20942, C₂₉×#20943, …
maximal normal subgroup of	C₂×C₂₉×#1882, C₂₉×#20942, C₂₉×#20943, …
maximal quotient of	C₂₉×#8953, C₂₉×#8955, C₂₉×#8971, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 614);