C₁₇×#1647 #14524653

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

Aliases

direct product

C₁₇×#1647

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₁₇×#547	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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)(18,19)(20,22)(21,24)(23,25)(26,27,31,35)(28,36,39,40)(29,34,30,33)(32,38,41,37);(19,22)(20,25)(23,24)(26,28,31,39)(27,32,35,41)(29,38,30,37)(33,40,34,36);(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×#1647, #17010160, #17010279, …
maximal subgroup of	C₂×C₁₇×#1647, C₁₇×#18503, C₁₇×#18516, …
maximal normal subgroup of	C₂×C₁₇×#1647, C₁₇×#18503, C₁₇×#18516, …
maximal quotient of	C₁₇×#7751, C₁₇×#7752, C₁₇×#7763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 379);