C₂×#117×C₅₉ #16837048

order	3776
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×#117×C₅₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₅₉	C₂²
commutator	C₂	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²	C₂⁴×C₅₉
socle	C₂³×C₅₉	C₂³
prime radical	C₂⁴×C₅₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₉ ◁ G

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 4 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)(9,12)(10,11)(13,14);(8,11)(12,14);(7,9,10,13)(8,12,11,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1458, C₅₉×#1464, C₅₉×#1729, …
maximal normal subgroup of	C₅₉×#1458, C₅₉×#1464, C₅₉×#1729, …
maximal quotient of	C₂×C₅₉×#376, C₂×C₄×C₂²⋊C₄×C₅₉, C₂×C₄×C₄⋊C₄×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 195);

C2×#117×C59 #16837048