C₂×C₂₉×#419 #16816608

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

Aliases

direct product

C₂×C₂₉×#419

Subgroups

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

752 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)(11,20)(12,15)(13,18)(17,21)(19,22);(7,9,12,19)(8,13,15,21)(10,18,11,17)(14,22,20,16);(7,10,12,11)(8,14,15,20)(9,17,19,18)(13,16,21,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10777, C₂₉×#10786, C₂₉×#10942, …
maximal normal subgroup of	C₂₉×#10777, C₂₉×#10786, C₂₉×#10942, …
maximal quotient of	C₂×C₂₉×#1479, C₂×C₂₉×#1491, C₂₉×#17449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1626);

C2×C29×#419 #16816608