C₁₇×#13433 #16871177

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13433

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#535	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,24)(20,28)(21,32)(22,35)(25,39)(26,41)(27,33)(29,45)(30,47)(31,44)(36,38)(37,40)(42,46)(43,48);(18,19,23,27)(20,29,31,25)(21,33,32,24)(22,36,35,26)(28,42,44,40)(30,37,48,46)(34,38,49,41)(39,47,45,43);(18,20,21,30,23,31,32,48)(19,25,24,37,27,29,33,46)(22,28,34,43,35,44,49,47)(26,40,38,39,36,42,41,45)

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6421);