C₁₇×#11539 #16869283

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11521
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11539

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
socle	C₂×C₁₇	#1467
prime radical	C₂³×C₁₇	C₂×M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₁₇×#405 ◁ G

270 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 102 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)(18,19,22,28,23,27,38,44,24,29,36,46,21,25,35,40)(20,30,32,47,33,43,48,45,34,39,37,49,31,26,41,42);(19,25,29,27)(22,36)(26,39,43,30)(28,40,46,44)(32,37)(35,38)(41,48)(42,49,45,47);(18,20,23,33,24,34,21,31)(19,26,25,39,29,43,27,30)(22,37,38,41,36,32,35,48)(28,45,40,47,46,42,44,49)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4527);