C₁₇×#13074 #16870818

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#13074

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

490 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 146 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)(20,30)(21,26,35,42)(22,37)(23,29)(24,40)(25,28)(27,31)(32,46,44,45)(33,39)(34,48,38,49)(36,47,41,43);(18,20,31,29,24,33,39,40,23,27,30,19,25,37,22,28)(21,32,46,42,36,48,34,47,35,44,45,26,41,49,38,43);(18,21)(19,26)(20,32)(22,38)(23,35)(24,36)(25,41)(27,44)(28,43)(29,42)(30,45)(31,46)(33,48)(34,39)(37,49)(40,47)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6062);