C₁₇×#11747 #16869491

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11747

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#102
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×#102
prime radical	C₁₇×#3169	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

368 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 2176

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

Conjugacy classes & character table

986 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4735);