C₁₇×#13340 #16871084

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13340
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13340

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#493
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#2011
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

552 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 118 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)(20,31)(21,28)(22,27)(23,41)(24,29)(25,32)(26,33)(30,37)(34,43)(35,49)(36,46)(38,48)(39,44)(40,47)(42,45);(18,20)(19,25)(21,36)(22,32)(23,42)(24,35)(26,41)(27,45)(28,31)(29,44)(30,46)(33,38)(34,37)(39,40)(43,47)(48,49);(18,20)(19,26)(21,33)(22,39)(23,42)(24,35)(25,30)(27,31)(28,43)(29,46)(32,40)(34,37)(36,38)(41,44)(45,48)(47,49)

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, 6328);