C₁₇×#7390 #16865134

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7389
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7390

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1333
commutator	C₁₆	C₂×C₈×C₁₇
Frattini, cosocle	#346	C₂²×C₁₇
prime radical	C₂×C₁₇×D₁₆	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₁₇×#346 ◁ G

128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 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)(18,19,21,28,23,30,34,48,25,31,40,29,24,42,22,41)(20,32,33,46,36,26,35,43,38,44,39,47,37,45,49,27);(19,26)(20,33)(21,22)(23,24)(27,41)(28,47)(29,46)(30,32)(31,45)(34,40)(35,37)(36,49)(38,39)(42,44)(43,48)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 378);