C₁₇×AGL(1,ℤ/16) #14525187

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#442
commutator	C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#509	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#97 ◁ G

154 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 72 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)(19,23,25,32)(20,27)(21,28)(24,30,33,26)(29,31);(18,19)(20,24)(21,30)(22,25)(23,31)(26,28)(27,32)(29,33);(18,20,28,31,22,29,21,27)(19,24,26,23,25,33,30,32)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×AGL(1,ℤ/16), #17187771, #17187780, …
maximal subgroup of	C₂×C₁₇×AGL(1,ℤ/16), C₁₇×#33468, C₁₇×#33469, …
maximal normal subgroup of	C₂×C₁₇×AGL(1,ℤ/16), C₁₇×#33468, C₁₇×#33469, …
maximal quotient of	C₁₇×#12065, C₁₇×#12067, C₁₇×#12077, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 913);