C₁₇×#9424 #16867168

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9424

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂×C₁₇×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 436 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) = 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)(18,19,24,27)(20,23,26,22)(21,28)(25,29)(30,32)(31,33)(34,35,39,43,40,42,38,36)(37,44,45,41,46,49,47,48);(18,20,22,19,24,26,23,27)(21,28,30,25,31,33,29,32)(34,36,39,42,40,43,38,35)(37,44,45,48,46,49,47,41);(18,21)(19,25)(20,28)(22,30)(23,29)(24,31)(26,33)(27,32)(34,37,40,46)(35,41,42,48)(36,44,43,49)(38,47,39,45)

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, 2412);