C₂×C₂₉×D₃₂ #16815973

order	3712
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₂₉×D₃₂

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₂₉
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

120 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);(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7537, C₂₉×#7541, C₄×C₂₉×D₃₂, …
maximal normal subgroup of	C₂₉×#7537, C₂₉×#7541, C₄×C₂₉×D₃₂, …
maximal quotient of	C₂×C₂₉×#1415, C₂×C₂₉×#1423, C₄×C₂₉×D₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 991);

C2×C29×D32 #16815973