C₁₇×#1617 #14524623

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1617

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂³×C₁₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 202 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) = 49
transitive degree	μ_t(G) = 544

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)(18,19,24,39)(20,29,31,46)(21,34,40,36)(22,27,23,28)(25,41,42,30)(26,38,49,37)(32,45,33,47)(35,43,48,44);(18,20,22,32)(19,25,27,43)(21,35,37,30)(23,33,24,31)(26,45,34,29)(28,44,39,42)(36,46,49,47)(38,41,40,48);(18,19,23,28)(20,25,33,44)(21,36,38,26)(22,27,24,39)(29,30,47,48)(31,42,32,43)(34,37,49,40)(35,46,41,45)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947146, #16947153, #16947160, …
maximal subgroup of	C₁₇×#12221, C₁₇×#12222, C₁₇×#12223, …
maximal normal subgroup of	C₁₇×#12221, C₁₇×#12222, C₁₇×#12223, …
maximal quotient of	C₁₇×#7792, C₁₇×#7794, C₁₇×#7806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 349);