D₄²×C₅₉ #16837079

order	3776
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

D₄²×C₅₉

Subgroups

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

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 944

A minimal faithful permutation representation — 4 generators on 67 points:

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

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×#1619, C₅₉×#1629, C₅₉×#1639, …
maximal normal subgroup of	C₅₉×#1619, C₅₉×#1629, C₅₉×#1639, …
maximal quotient of	D₄×C₂²⋊C₄×C₅₉, D₄×C₄⋊C₄×C₅₉, C₅₉×#2358, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 226);

D42×C59 #16837079