C₂×SD₃₂×C₅₉ #16837040

order	3776
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂×SD₃₂×C₅₉

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₅₉
prime radical	C₂×D₈×C₅₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂×C₈×C₅₉ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 77 points:

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

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×SD₃₂×C₅₉, C₅₉×#2175, C₅₉×#2185, …
maximal normal subgroup of	C₄×SD₃₂×C₅₉, C₅₉×#2175, C₅₉×#2185, …
maximal quotient of	C₂×C₅₉×#357, C₂×C₅₉×#358, C₂×C₅₉×#367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 187);

C2×SD32×C59 #16837040