C₁₇×#1663 #14524669

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1663

Subgroups

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

172 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 49
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,28)(20,29,31,32)(21,30,25,33)(22,27,23,26)(34,35,39,37)(36,42,45,49)(38,46,48,41)(40,47,43,44);(18,20)(19,25)(21,28)(22,33)(23,30)(24,31)(26,32)(27,29)(34,36,39,45)(35,40,37,43)(38,47,48,44)(41,49,46,42);(18,21,24,25)(19,20,28,31)(22,32,23,29)(26,30,27,33)(34,37,39,35)(36,43,45,40)(38,41,48,46)(42,47,49,44)

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922173, D₁₇×#1663, #17015525, …
maximal subgroup of	C₁₇×#7526, C₂×C₁₇×#1663, C₁₇×#18990, …
maximal normal subgroup of	C₁₇×#7526, C₂×C₁₇×#1663, C₁₇×#18990, …
maximal quotient of	C₁₇×#7763, C₁₇×#7768, C₁₇×#7772, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 395);