C₁₇×#11522 #16869266

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11522
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11522

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	C₂⁴×C₁₇	M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 284 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)(18,19,21,27,22,28,34,44,23,26,33,42,35,25,39,41)(20,29,31,43,32,40,46,49,30,24,36,38,45,37,47,48);(18,20)(19,24)(21,31)(22,32)(23,30)(25,40)(26,29)(27,43)(28,37)(33,36)(34,46)(35,45)(38,42)(39,47)(41,48)(44,49);(19,25,26,28)(20,30)(21,33)(24,37,29,40)(27,44,42,41)(32,45)(34,39)(38,49,43,48)

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, 4510);