C₂₉×#2488 #16816202

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2488

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2488, C₂₉×#34754, C₂₉×#34763, …
maximal normal subgroup of	C₂×C₂₉×#2488, C₂₉×#34754, C₂₉×#34763, …
maximal quotient of	C₂₉×#13874, C₂₉×#13896, C₂₉×#13992, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1220);

C29×#2488 #16816202