C₁₇×#1689 #14524695

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1689

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₂×D₄×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 166 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)(18,19)(20,22)(21,24)(23,25)(26,27,30,33)(28,34,36,41)(29,38,35,32)(31,39,40,37);(26,28,35,39,30,36,29,37)(27,31,38,41,33,40,32,34);(19,22)(20,25)(23,24)(28,36)(31,40)(34,41)(37,39)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947816, #16947823, #16947984, …
maximal subgroup of	C₁₇×#12326, C₁₇×#12327, C₁₇×#12350, …
maximal normal subgroup of	C₁₇×#12326, C₁₇×#12327, C₁₇×#12350, …
maximal quotient of	C₁₇×#8652, C₁₇×#9227, C₁₇×#9569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 421);