C₁₇×#23468 #16881212

order	4352
nilpotency class	3
isoclinism	isoclinic class of #23444
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#23468

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
prime radical	C₂³×D₄×C₁₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

1506 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1506 conjugacy classes of subgroups — too many to draw. Only its 334 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 — 4 generators on 41 points:

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

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, 16456);