C₁₇×#13464 #16871208

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13357
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#13464

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×Q₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	#120
LCS	G ▷ C₂²×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×Q₈×C₁₇ ◁ G

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

normal subgroups only

This group has 416 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) = 41
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6452);