C₁₇×#1861 #14524867

order	2176
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1861

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#120
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂×C₁₇	#385
prime radical	C₂×#41×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

262 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 108 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)(18,19,23,27,24,28,22,30)(20,29,26,25,32,33,31,21);(18,20,23,26,24,32,22,31)(19,25,27,33,28,21,30,29);(18,21)(19,26)(20,30)(22,33)(23,29)(24,25)(27,32)(28,31)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1861, #17035225, #17040283, …
maximal subgroup of	C₂×C₁₇×#1861, C₁₇×#20867, C₁₇×#21477, …
maximal normal subgroup of	C₂×C₁₇×#1861, C₁₇×#20867, C₁₇×#21477, …
maximal quotient of	C₁₇×#8839, C₁₇×#8840, C₁₇×#8841, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 593);