C₁₇×#7366 #16865110

order	4352
nilpotency class	5
isoclinism	isoclinic class of #1414
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7366

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#354
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	#382	C₂²×C₁₇
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#382 ◁ G

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

normal subgroups only

This group has 158 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(26,27)(28,36,38,49)(29,40,41,56)(30,43,44,34)(31,35)(32,37,45,52)(33,42)(39,51,55,50)(46,53,47,54)(48,57);(26,28,30,38,31,39,44,55)(27,32,34,46,35,47,43,45)(29,37,42,53,41,54,57,52)(33,36,40,50,48,51,56,49)

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, 354);