C₁₇×#9514 #16867258

order	4352
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#9514

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#386
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 478 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)(20,23,27,30)(21,24)(22,25)(26,29,32,33)(28,31)(34,35,38,42,39,36,40,44)(37,43,46,49,45,41,47,48);(18,20,22,27)(19,23)(21,26,28,32)(24,29)(25,30)(31,33)(34,36,38,44,39,35,40,42)(37,43,47,48,45,41,46,49);(18,21,22,28)(19,24,25,31)(20,26,27,32)(23,29,30,33)(34,37)(35,41)(36,43)(38,47)(39,45)(40,46)(42,49)(44,48)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2502);