C₁₇×#10209 #16867953

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#10209

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#3214	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

474 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 94 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)(20,27)(21,31)(22,25)(23,26)(24,28)(29,32)(30,33)(36,43)(37,38)(40,44)(41,47)(45,46)(48,49);(18,20,23,29)(19,24,26,33)(21,30,22,28)(25,32,31,27)(34,35)(36,44)(37,41)(38,47)(39,42)(40,46)(43,48)(45,49);(20,28)(21,22)(24,32)(25,31)(27,33)(29,30)(34,36)(35,40)(37,46)(38,43)(39,45)(41,49)(42,48)(44,47)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3197);