C₂₉×#2382 #16816096

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2382

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

408 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 3712

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8912, C₂₉×#8913, C₂₉×#8915, …
maximal normal subgroup of	C₂₉×#8912, C₂₉×#8913, C₂₉×#8915, …
maximal quotient of	C₂₉×#13829, C₂₉×#13833, C₂₉×#14385, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1114);