C₁₇×#10628 #16868372

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10628

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#397
prime radical	C₂³×C₁₇	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

292 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 106 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)(26,27)(28,36,39,49)(29,33)(30,34)(31,35)(32,38,46,43)(37,52,40,51)(41,47)(42,48)(44,50)(45,54,56,53)(55,57);(18,19,21,24)(20,22,25,23)(26,28)(27,32)(29,40)(30,43)(31,39)(33,45)(34,49)(35,46)(36,50)(37,42)(38,44)(41,53)(47,52)(48,56)(51,57)(54,55);(19,22)(20,25)(23,24)(26,29,30,41,31,42,44,55)(27,33,34,47,35,48,50,57)(28,37,38,53,39,40,43,54)(32,45,36,51,46,56,49,52)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3616);