C₁₇×#13720 #16871464

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#13720

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

182 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 57 points:

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

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6708);