C₂²×M₁₆×C₅₉ #16837100

order	3776
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂²×M₁₆×C₅₉

Subgroups

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

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 4 generators on 71 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1728, C₅₉×#1729, C₂×C₅₉×H(3,ℤ/4), …
maximal normal subgroup of	C₅₉×#1728, C₅₉×#1729, C₂×C₅₉×H(3,ℤ/4), …
maximal quotient of	C₂²×#97×C₅₉, C₂×C₄×M₁₆×C₅₉, C₂²×C₂²⋊C₈×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 247);

C22×M16×C59 #16837100