C₁₇×#10560 #16868304

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10560

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#394
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₁₇×#3192	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

490 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 41 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)(27,32)(28,35)(29,30)(33,40)(34,38)(36,37);(18,20)(19,22)(21,24)(23,25)(26,27)(28,33)(29,38)(30,32)(31,34)(35,39)(36,41)(37,40);(22,25)(26,28,29,36,31,37,30,35)(27,33,32,39,34,40,38,41)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3548);