C₁₇×#10382 #16868126

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#10382

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂×C₁₇×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

446 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 90 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)(20,22)(21,24)(23,25)(26,27)(28,34,36,40)(29,32)(30,33)(31,37,35,38)(39,41);(20,25)(22,23)(26,27)(28,35,36,31)(29,32)(30,33)(34,37,40,38)(39,41);(19,22)(20,25)(23,24)(26,28)(27,31)(29,38)(30,36)(32,40)(33,35)(34,41)(37,39)

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, 3370);