C₁₇×#737 #13063388

order	1377
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃³×C₁₇ · Schur multiplier (H₂) = C₃²

Aliases

direct product

C₁₇×#737

Subgroups

	subgroup	G/H
center	C₉×C₁₇	C₃²
commutator, Frattini, cosocle	C₃	C₃³×C₁₇
socle	C₃×C₁₇	C₃³
prime radical	C₁₇×H(3,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₇ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 459

A minimal faithful permutation representation — 3 generators on 44 points:

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

Conjugacy classes & character table

561 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×#6872, C₁₇×#6873, C₁₇×#6903, …
maximal normal subgroup of	C₁₇×#6872, C₁₇×#6873, C₁₇×#6903, …
maximal quotient of	C₁₇×#6887, C₉×C₁₇×H(3,𝔽₃), C₉×C₁₇×3₋¹⁺², …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1377, 14);

C17×#737 #13063388