C₁₇×#7466 #16865210

order	4352
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7466

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₄²
commutator	C₄	C₄×C₁₆×C₁₇
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₇
socle	C₂²×C₁₇	#346
prime radical	C₂³×C₁₇	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ G

182 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 53
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,31,26,33,37,46,27,29,38,41,39,42,50,51,28,32,36,45,40,47,49,53,24,30,34,43,35,44,48,52);(19,21)(23,29,32,30)(25,36)(31,43,45,41)(33,42,47,44)(34,38)(37,49)(46,52,53,51)(48,50)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 454);