C₁₇×#10026 #16867770

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10026
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#10026

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 564 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) = 41
transitive degree	μ_t(G) = 1088

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)(20,22)(21,24)(23,25)(26,27)(28,34)(29,37)(30,33)(31,36)(32,39)(35,41)(38,40);(19,22)(20,25)(23,24)(31,40)(34,41);(18,19)(20,23)(21,24)(22,25)(26,28)(27,31)(29,38)(30,35)(32,41)(33,40)(34,37)(36,39)

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, 3014);