C₁₇×#10635 #16868379

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10631
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10635

Subgroups

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

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

normal subgroups only

This group has 294 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)(19,22)(23,25)(26,27,31,36,32,37,30,35)(28,38,41,33,42,49,40,50)(29,43,45,51,46,52,47,34)(39,54,55,57,44,48,56,53);(19,23)(21,24)(22,25)(26,28,32,42)(27,33,37,50)(29,44,46,39)(30,41,31,40)(34,48,51,54)(35,49,36,38)(43,57,52,53)(45,55,47,56);(18,19)(20,22)(21,25)(23,24)(26,29,30,45,32,46,31,47)(27,34,35,43,37,51,36,52)(28,39,40,55,42,44,41,56)(33,48,38,53,50,54,49,57)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3623);