C₁₇×#33981 #16891725

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#33981

Subgroups

	subgroup	G/H
center	C₄×C₁₇	C₂×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₁₇
socle	C₂×C₁₇	C₂²×D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂²×C₁₆×C₁₇ ◁ G

466 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 202 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) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,31)(21,27)(22,40)(23,44)(24,26)(25,33)(28,42)(29,38)(30,39)(32,59)(34,64)(35,66)(36,58)(37,67)(41,56)(43,72)(45,54)(46,53)(47,63)(48,60)(49,74)(50,76)(51,71)(52,69)(55,80)(57,62)(61,78)(65,81)(68,77)(70,73)(75,79);(18,20)(19,25)(21,32)(22,41)(23,45)(24,36)(26,47)(27,48)(28,54)(29,56)(30,57)(31,40)(33,42)(34,38)(35,39)(37,68)(43,75)(44,49)(46,61)(50,78)(51,79)(52,64)(53,77)(55,81)(58,72)(59,67)(60,69)(62,80)(63,76)(65,71)(66,73)(70,74);(19,26)(25,47)(27,30)(28,50)(29,51)(31,58)(40,72)(44,53)(48,57)(49,77)(52,55)(54,78)(56,79)(59,66)(64,81)(67,73);(18,21,24,39)(19,27,26,30)(20,32,36,35)(22,37,43,70)(23,38,46,71)(25,48,47,57)(28,52,50,55)(29,53,51,44)(31,59,58,66)(33,60,63,62)(34,61,65,45)(40,67,72,73)(41,68,75,74)(42,69,76,80)(49,56,77,79)(54,64,78,81)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26969);