C₁₇×#9982 #16867726

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9980
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#9982

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂²×#41×C₁₇	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 722 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)(21,23)(24,25)(26,27,32,37)(28,38,41,49)(29,34,45,52)(30,36,31,35)(33,42,48,40)(39,54,55,50)(43,57,56,47)(44,53,46,51);(22,25)(26,28)(27,33)(29,43)(30,42)(31,40)(32,41)(34,50)(35,49)(36,38)(37,48)(39,44)(45,56)(46,55)(47,51)(52,54)(53,57);(18,20)(19,22)(21,24)(23,25)(26,29,32,45)(27,34,37,52)(28,39,41,55)(30,44,31,46)(33,47,48,57)(35,51,36,53)(38,50,49,54)(40,43,42,56)

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, 2970);