C₁₇×#13077 #16870821

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13077

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3060	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

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

normal subgroups only

This group has 470 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)(20,30,33,45)(21,26,36,44)(22,37)(23,29)(24,42)(25,32,43,38)(27,31)(28,41)(34,35,48,39)(40,49)(46,47);(18,20,31,44,41,48,22,38,23,33,47,26,24,34,40,32)(19,25,37,35,42,21,27,45,29,43,49,39,28,36,46,30);(18,21)(19,26)(20,27)(22,39)(23,36)(24,25)(28,38)(29,44)(30,47)(31,45)(32,42)(33,46)(34,37)(35,40)(41,43)(48,49)

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, 6065);