C₁₇×#21827 #16879571

order	4352
nilpotency class	3
isoclinism	isoclinic class of #17405
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#21827

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₂²⋊C₄×C₁₇ ◁ G

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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 — 4 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)(21,32,35,25)(22,26)(23,27)(24,31)(29,43,44,40)(30,38)(33,47,48,37)(34,46,49,41)(36,42)(39,45);(18,20,22,31)(19,24,26,28)(21,33,34,29)(23,30,36,45)(25,40,41,37)(27,39,42,38)(32,43,46,47)(35,48,49,44);(18,21,22,34)(19,25,26,41)(20,29,31,33)(23,35,36,49)(24,37,28,40)(27,32,42,46)(30,44,45,48)(38,43,39,47);(19,26)(20,30)(24,38)(25,41)(27,42)(28,39)(29,44)(31,45)(32,46)(33,48)(37,43)(40,47)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 14815);