C₁₇×#21796 #16879540

order	4352
nilpotency class	3
isoclinism	isoclinic class of #17405
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₇×#21796

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#537	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄⋊C₄×C₁₇ ◁ G

1334 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 366 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 — 4 generators on 41 points:

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 14784);