C₁₇×#13360 #16871104

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13360
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13360

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₇
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

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

normal subgroups only

This group has 702 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) = 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)(20,29)(21,34)(22,25)(23,28)(24,31)(26,38)(27,39)(30,47)(32,46)(33,44)(35,42)(36,45)(37,43)(40,49)(41,48);(18,20)(19,24)(21,35)(22,30)(23,33)(25,41)(26,44)(27,40)(28,42)(29,34)(31,38)(32,39)(36,49)(37,48)(43,46)(45,47);(19,25)(20,30)(22,39)(26,43)(27,28)(29,44)(31,49)(32,33)(34,45)(35,48)(36,37)(40,41)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6348);