C₂×C₂₉×#416 #16816606

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₂₉×#416

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂×D₄
prime radical	C₂²×#41×C₂₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4,5,6)(7,8)(9,16)(10,14)(11,19)(12,15)(13,17)(18,21)(20,22);(7,9)(8,13)(10,17)(11,20)(12,18)(14,21)(15,22)(16,19);(7,10,12,11)(8,14,15,19)(9,17,18,20)(13,21,22,16)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#10779, C₂₉×#10782, C₂₉×#10791, …
maximal normal subgroup of	C₂₉×#10779, C₂₉×#10782, C₂₉×#10791, …
maximal quotient of	C₂×C₂₉×#1476, C₂×C₂₉×#1488, C₂₉×#17443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1624);

C2×C29×#416 #16816606