C₁₇×#7433 #16865177

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7396
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7433

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#353
commutator	C₂×M₁₆	C₂×C₄×C₁₇
Frattini, cosocle	#407	C₂²×C₁₇
socle	C₂×C₁₇	#1352
prime radical	C₂⁴×C₁₇	Q₁₆
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#407 ◁ G

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

normal subgroups only

This group has 182 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)(18,19,22,26,23,28,30,27)(20,29,32,46,34,47,33,42)(21,35,37,43,39,45,38,25)(24,36,40,48,41,49,44,31);(18,20,30,32,23,34,22,33)(19,24,26,40,28,41,27,44)(21,36,37,48,39,49,38,31)(25,42,45,29,43,46,35,47)

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 421);