C₁₇×#10935 #16868679

order	4352
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₇×#10935

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#120
commutator	C₂³	C₂×C₄²×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂⁶×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

2594 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 2594 conjugacy classes of subgroups — too many to draw. Only its 302 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) = 544

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)(19,21)(26,27)(28,32,33,30)(29,31);(22,23,24,25)(26,28)(27,30)(29,33)(31,32);(18,19,20,21)(26,27)(28,30)(29,31)(32,33)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3923);