C₁₇×#1649 #14524655

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

Aliases

direct product

C₁₇×#1649

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

234 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 76 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)(26,27,32,36)(28,37,29,40)(30,35,31,34)(33,39,41,38);(19,22)(20,25)(23,24)(26,28,32,29)(27,33,36,41)(30,39,31,38)(34,40,35,37);(26,29,32,28)(27,33,36,41)(30,38,31,39)(34,40,35,37)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1649, #17010172, #17010281, …
maximal subgroup of	C₂×C₁₇×#1649, C₁₇×#18503, C₁₇×#18516, …
maximal normal subgroup of	C₂×C₁₇×#1649, C₁₇×#18503, C₁₇×#18516, …
maximal quotient of	C₁₇×#7756, C₁₇×#7757, C₁₇×#7763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 381);