C₂×C₂₉×M₆₄ #16815971

order	3712
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂×C₂₉×M₆₄

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₂₉	C₂²
commutator	C₂	C₂²×C₁₆×C₂₉
Frattini, cosocle	C₁₆	C₂³×C₂₉
socle	C₂²×C₂₉	C₂×C₁₆
prime radical	C₂³×C₂₉	C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₂₉ ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 63 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63);(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);(4,20)(6,22)(8,24)(10,26)(12,28)(14,30)(16,32)(18,34)

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7466, C₂₉×#7467, C₂₉×#7468, …
maximal normal subgroup of	C₂₉×#7466, C₂₉×#7467, C₂₉×#7468, …
maximal quotient of	C₂×C₂₉×#1397, C₄×C₂₉×M₆₄, C₂×C₂₉×C₂²⋊C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 989);

C2×C29×M64 #16815971