C₁₇×#11580 #16869324

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#11580

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

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

normal subgroups only

This group has 552 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) = 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)(18,19,21,25,22,24,20,23)(26,27,30,34,31,35,29,33)(28,32,36,39,37,40,38,41);(18,20,22,21)(19,23)(24,25)(26,28)(27,32)(29,38)(30,36)(31,37)(33,41)(34,39)(35,40);(26,29,31,30)(27,33,35,34)(28,36,37,38)(32,39,40,41)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4568);