C₁₇×#7201 #16864945

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7201

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#95
commutator	C₂³	C₄×C₈×C₁₇
Frattini, cosocle	C₂³×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#336
prime radical	C₂⁴×C₁₇	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

286 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 102 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)(26,27,29,35,32,28,33,37,31,34,30,40,39,36,41,38);(18,20)(19,22)(21,25)(23,24)(26,28,30,37,32,34,41,40,31,36,29,38,39,27,33,35)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 189);