C₁₇×#11524 #16869268

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×#11524

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
socle	C₂×C₁₇	#1464
prime radical	C₂×#41×C₁₇	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

288 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 98 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)(18,19,22,28,23,27,38,44,24,29,37,45,21,26,35,43)(20,30,33,46,32,25,39,41,31,40,36,48,34,42,47,49);(18,20)(19,25)(21,34)(22,36)(23,32)(24,31)(26,30)(27,40)(28,41)(29,42)(33,37)(35,39)(38,47)(43,46)(44,48)(45,49);(19,26,29,27)(20,31)(22,37)(25,40,42,30)(28,44,45,43)(32,34)(35,38)(41,46,49,48)

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, 4512);