C₁₇×#10022 #16867766

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10022

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#2631	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

576 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 98 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)(18,19,22,29)(20,24,31,26)(21,25,34,43)(23,30,36,28)(27,37,44,35)(32,41,45,40)(33,48,46,42)(38,49,39,47);(19,24)(20,31)(21,34)(25,42)(26,29)(27,38)(28,40)(30,41)(32,45)(35,37)(39,44)(43,48);(19,25)(20,32)(21,35)(24,38)(26,39)(27,28)(29,43)(30,44)(31,45)(33,46)(34,37)(40,42)(41,48)(47,49)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3010);