C₁₇×#7441 #16865185

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₇×#7441

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1353
commutator	C₂×M₁₆	C₂×C₄×C₁₇
Frattini, cosocle	#423	C₂²×C₁₇
prime radical	C₂³×C₁₇	#104
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#423 ◁ G

136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 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)(20,28,30,40,32,45,31,48)(21,25,34,41)(22,36)(23,26)(24,29,38,46,39,47,44,33)(27,37)(35,43,49,42);(18,20)(19,24,26,39)(21,33,34,46)(22,31)(23,32)(25,40)(27,38,36,44)(28,43)(29,35,47,49)(30,37)(41,48)(42,45)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 429);