C₁₇×#8101 #16865845

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8101
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#8101

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#95
commutator	C₂³	C₂×C₄²×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂⁶×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁶×C₁₇ ◁ G

2414 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 278 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,31)(21,24)(22,25)(23,27,30,33)(29,32);(18,20)(19,23,25,31)(21,28)(22,27)(24,30,32,26)(29,33);(19,24)(23,30)(25,32)(26,31)

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, 1089);