C₁₇×#10216 #16867960

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10216

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 1088

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3204);