C₁₇×#11734 #16869478

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11734

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×#99
prime radical	C₂²×D₄×C₁₇	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

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

normal subgroups only

This group has 434 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)(19,23,24,25)(26,27,29,33,30,31,36,38)(28,32,34,39,35,37,40,41);(18,19)(20,23)(21,25)(22,24)(27,31)(32,37);(18,20,22,21)(19,23,24,25)(26,28,30,35)(27,32,31,37)(29,34,36,40)(33,39,38,41)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4722);