C₁₇×#32899 #16890643

order	4352
nilpotency class	3
isoclinism	isoclinic class of #32898
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₁₇×#32899

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

3866 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 3866 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) = 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)(27,33)(34,37);(22,23)(24,27)(25,28)(26,29)(30,34)(31,33)(32,35)(36,37);(22,24)(23,27)(25,30)(26,31)(28,34)(29,33)(32,36)(35,37);(19,21)(22,25,26,32)(23,28,29,35)(24,30,31,36)(27,34,33,37)

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, 25887);