C₁₇×#13658 #16871402

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13657
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#13658

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2177
commutator	C₁₆	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#2263	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₁₇×#346 ◁ G

194 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 82 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)(19,25,27,41)(20,30)(21,33)(22,37)(23,31)(26,34,38,42)(28,40,45,44)(29,46,39,43)(32,36)(35,47)(48,49);(18,19)(20,26)(21,34)(22,38)(23,39)(24,27)(25,32)(28,37)(29,31)(30,45)(33,41)(35,40)(36,42)(43,49)(44,48)(46,47);(18,20,31,37,24,22,23,30)(19,26,29,28,27,38,39,45)(21,33,48,47,36,32,35,49)(25,40,43,34,41,44,46,42)

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, 6646);