C₁₇×#10385 #16868129

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10385

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

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

normal subgroups only

This group has 396 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)(18,19,21,24)(20,26)(22,25,30,32)(23,31)(27,28)(29,33)(34,35)(36,39)(37,44,46,40)(38,41)(42,47,45,49)(43,48);(18,19)(20,27,29,23)(21,24)(22,25)(26,28,33,31)(30,32)(34,36,38,43)(35,39,41,48)(37,45)(40,49)(42,46)(44,47);(18,20)(19,23)(21,29)(22,31)(24,27)(25,33)(26,32)(28,30)(34,37,38,46)(35,40,41,44)(36,42,43,45)(39,47,48,49)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3373);