C₁₇×#7202 #16864946

order	4352
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7202

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₂²⋊C₄
commutator	C₂×C₄	C₄×C₈×C₁₇
Frattini, cosocle	C₂³×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#336
prime radical	C₂⁴×C₁₇	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 304 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 — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(26,27,30,35,33,34,41,39,32,36,31,28,29,38,40,37);(18,20)(19,22)(21,25)(23,24)(26,28,31,34,33,37,40,36,32,35,30,38,29,39,41,27)

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 190);