C₂₉×#2399 #16816113

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2399

Subgroups

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

504 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 248 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)(34,35,38,41)(36,40,37,39)(42,43,46,49)(44,48,45,47);(30,31)(32,33)(34,36,38,37)(35,39,41,40)(42,44,46,45)(43,47,49,48);(31,33)(34,36,38,37)(35,40,41,39)(42,45,46,44)(43,48,49,47);(34,37,38,36)(35,39,41,40)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9030, C₂₉×#10014, C₂₉×#10017, …
maximal normal subgroup of	C₂₉×#9030, C₂₉×#10014, C₂₉×#10017, …
maximal quotient of	C₂₉×#13848, C₂₉×#13850, C₂₉×#13856, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1131);