C₁₇×#1791 #14524797

order	2176
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#1791

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#120
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂×C₁₇	#379
prime radical	C₁₇×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 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)(18,19,22,27,23,26,35,40)(20,28,31,41,30,24,34,37)(21,25,33,38,32,39,45,49)(29,36,44,47,43,42,46,48);(18,20)(19,24)(21,29)(22,34)(23,30)(25,36)(26,28)(27,41)(31,35)(32,43)(33,46)(37,40)(38,48)(39,42)(44,45)(47,49);(18,21)(19,25)(20,29)(22,33)(23,32)(24,36)(26,39)(27,38)(28,42)(30,43)(31,44)(34,46)(35,45)(37,47)(40,49)(41,48)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16951609, #16951616, #16951643, …
maximal subgroup of	C₁₇×#13045, C₁₇×#13046, C₁₇×#13051, …
maximal normal subgroup of	C₁₇×#13045, C₁₇×#13046, C₁₇×#13051, …
maximal quotient of	C₁₇×#8316, C₁₇×#8317, C₁₇×#8348, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 523);