C₁₇×#7190 #16864934

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7190

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂×C₄	C₄×C₈×C₁₇
Frattini, cosocle	C₂×#117	C₂²×C₁₇
socle	C₂²×C₁₇	#342
prime radical	C₂⁴×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

322 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 110 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)(28,36,38,48)(29,40,41,33)(30,43)(31,35)(32,37)(34,44)(39,53,52,49)(42,47,55,54)(45,57)(46,51)(50,56);(26,28,30,39,31,38,44,52)(27,32,34,45,35,46,43,56)(29,37,42,50,41,51,55,57)(33,36,47,49,40,48,54,53)

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, 178);