C₁₇×#1650 #14524656

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1650

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₂×D₄×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

200 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 68 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)(20,21)(24,25)(26,27,31,35)(28,36,39,40)(29,34,30,33)(32,38,41,37);(18,19)(20,23)(21,25)(22,24)(26,28,31,39)(27,32,35,41)(29,38,30,37)(33,40,34,36);(18,20,22,21)(19,23,24,25)(27,33)(29,30)(32,40)(34,35)(36,41)(37,38)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1650, #17010174, #17010341, …
maximal subgroup of	C₂×C₁₇×#1650, C₁₇×#18503, C₁₇×#18520, …
maximal normal subgroup of	C₂×C₁₇×#1650, C₁₇×#18503, C₁₇×#18520, …
maximal quotient of	C₁₇×#7775, C₁₇×#7777, C₁₇×#7779, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 382);