C₁₇×#11394 #16869138

order	4352
nilpotency class	3
isoclinism	isoclinic class of #2032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#11394

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#393
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

1090 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 254 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

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

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, 4382);