C₁₇×#10389 #16868133

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10386
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10389

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 1088

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

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3377);