C₂³×Q₈×C₅₉ #16837115

order	3776
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂³×Q₈×C₅₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅₉	C₂²
commutator, Frattini, cosocle	C₂	C₂⁵×C₅₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₉ ◁ G

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 5 generators on 73 points:

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

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×#1446, C₅₉×#1784, C₅₉×#1787, …
maximal normal subgroup of	C₅₉×#1446, C₅₉×#1784, C₅₉×#1787, …
maximal quotient of	C₂³×C₄⋊C₄×C₅₉, C₂²×C₄×Q₈×C₅₉, C₂²×C₂²⋊Q₈×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 262);

C23×Q8×C59 #16837115