C₂₉×#1985 #16815699

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1985

Subgroups

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

280 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 136 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 — 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)(36,40)(37,38)(39,41)(42,43,47,48,46,49,45,44);(30,31,32,33)(35,38)(39,40)(42,44,45,49,46,48,47,43);(34,36,37,41)(35,39,38,40)(42,45,46,47)(43,48,49,44)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7061, C₂₉×#7133, C₂₉×#7284, …
maximal normal subgroup of	C₂₉×#7061, C₂₉×#7133, C₂₉×#7284, …
maximal quotient of	C₂₉×#9867, C₂₉×#9868, C₂₉×#9869, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 717);