C₁₇×#32900 #16890644

order	4352
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₁₇×#32900

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
prime radical	C₂²×C₁₇×H(5,𝔽₂)	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

4032 conjugacy classes of subgroups; only the 370 normal subgroups are shown.

normal subgroups only

This group has 4032 conjugacy classes of subgroups — too many to draw. Only its 370 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 — 4 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)(22,23,26,29)(24,27,31,34)(25,28,32,35)(30,36,37,33);(22,24)(23,27)(25,30)(26,31)(28,33)(29,34)(32,37)(35,36);(22,25)(23,28)(24,30)(26,32)(27,33)(29,35)(31,37)(34,36);(19,21)

Conjugacy classes & character table

833 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 25888);