C₁₇×#1661 #14524667

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1661

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₁₇×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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)(19,22)(20,24)(23,25)(26,27,31,35)(28,36,38,41)(29,34,30,33)(32,39,40,37);(20,24)(22,25)(26,28)(27,32)(29,39)(30,37)(31,38)(33,41)(34,36)(35,40);(18,19,21,23)(20,25,24,22)(26,28)(27,32)(29,37)(30,39)(31,38)(33,36)(34,41)(35,40)

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1661, #17015483, #17015503, …
maximal subgroup of	C₂×C₁₇×#1661, C₁₇×#18984, C₁₇×#18987, …
maximal normal subgroup of	C₂×C₁₇×#1661, C₁₇×#18984, C₁₇×#18987, …
maximal quotient of	C₁₇×#7752, C₁₇×#7753, C₁₇×#7756, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 393);