C₁₇×#7534 #16865278

order	4352
nilpotency class	6
isoclinism	isoclinic class of #7533
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7534

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1409
commutator	C₄×C₈	C₂×C₄×C₁₇
Frattini, cosocle	#494	C₂²×C₁₇
prime radical	C₂²×C₁₇	#353
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#494 ◁ G

128 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 30 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)(18,19,21,27,24,29,37,44)(20,26,31,42,33,40,47,49)(22,28,36,45,23,38,35,43)(25,34,39,30,41,46,48,32);(19,25,29,41)(20,30)(22,23)(26,38,40,28)(27,42,44,49)(31,46)(32,33)(34,47)(35,36)(39,45,48,43)

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 522);