C₁₇×#7494 #16865238

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7493
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7494

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1390
commutator	C₂×D₄	C₄²×C₁₇
Frattini, cosocle	#532	C₂²×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#532 ◁ G

270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,27)(20,30,32,44)(22,38,36,46)(23,28,40,26)(24,29,37,45)(25,34,41,48)(31,43,39,47)(33,49,35,42);(18,20,22,33,24,34,23,39)(19,25,28,42,29,44,38,43)(21,35,36,48,37,31,40,32)(26,41,45,49,46,30,27,47)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 482);