C₁₇×#13710 #16871454

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13709
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#13710

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2226
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#508	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

160 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 70 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)(19,26)(20,30,33,48)(21,24)(22,35)(23,29)(27,43,32,49)(28,37)(31,44,40,46)(34,45)(36,39,47,41)(38,42);(18,19,24,23,25,29,21,26)(20,27,40,39,33,32,31,41)(22,28,37,35,38,45,34,42)(30,36,44,49,48,47,46,43);(18,20)(19,27)(21,31)(22,36)(23,39)(24,40)(25,33)(26,41)(28,44)(29,32)(30,42)(34,43)(35,48)(37,49)(38,47)(45,46)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6698);