C₁₇×#8126 #16865870

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8101
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#8126

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#95
commutator	C₂³	C₂×C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

520 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 1088

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 1114);