C₁₇×#1621 #14524627

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

Aliases

direct product

C₁₇×#1621

Subgroups

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

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

normal subgroups only

This group has 278 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) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 33 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)(27,30)(28,32)(31,33);(19,22)(20,25)(23,24)(28,32)(30,33);(26,27,29,31)(28,33,32,30)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1621, #17010215, #17010269, …
maximal subgroup of	C₂×C₁₇×#1621, C₁₇×#18510, C₁₇×#18516, …
maximal normal subgroup of	C₂×C₁₇×#1621, C₁₇×#18510, C₁₇×#18516, …
maximal quotient of	C₁₇×#7735, C₁₇×#7737, C₁₇×#7740, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 353);