C₁₇×#13719 #16871463

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#13719

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 202 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) = 2176

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)(27,28)(29,30)(31,41)(32,47)(34,38)(35,50)(36,49)(37,40)(39,52)(42,56)(43,46)(44,45)(48,55)(51,54)(53,57);(19,22)(23,25)(26,27,30,34,31,35,44,49,47,52,56,57,55,54,43,40,33,37,46,51,48,53,42,39,32,36,45,50,41,38,29,28);(18,20,21,24)(19,23,22,25)(26,28,29,38,41,50,45,36,32,39,42,53,48,51,46,37,33,40,43,54,55,57,56,52,47,49,44,35,31,34,30,27)

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, 6707);