C₂×C₂₉×Q₆₄ #16815975

order	3712
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂×C₂₉×Q₆₄

Subgroups

	subgroup	G/H
center, socle, prime radical	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

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 95 points:

(1,2)(67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(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)(35,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36);(3,35,19,51)(4,36,20,52)(5,37,21,53)(6,38,22,54)(7,39,23,55)(8,40,24,56)(9,41,25,57)(10,42,26,58)(11,43,27,59)(12,44,28,60)(13,45,29,61)(14,46,30,62)(15,47,31,63)(16,48,32,64)(17,49,33,65)(18,50,34,66)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7538, C₂₉×#7542, C₄×C₂₉×Q₆₄, …
maximal normal subgroup of	C₂₉×#7538, C₂₉×#7542, C₄×C₂₉×Q₆₄, …
maximal quotient of	C₂×C₂₉×#1416, C₂×C₂₉×#1423, C₄×C₂₉×Q₆₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 993);

C2×C29×Q64 #16815975