C₁₇×#10623 #16868367

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10260
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10623

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

350 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 4352

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3611);