C₁₇×#7364 #16865108

order	4352
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7364

Subgroups

	subgroup	G/H
center	C₈×C₁₇	#99
commutator	C₂×C₄	C₂×C₁₆×C₁₇
Frattini, cosocle	C₂×M₃₂	C₂²×C₁₇
socle	C₂×C₁₇	#1322
prime radical	C₂³×C₁₇	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₇×M₃₂ ◁ G

126 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 54 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 352);