C₁₇×#2027 #14525033

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2027

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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)(18,19,21,23)(20,24,25,22)(26,27)(28,30)(29,32)(31,33);(18,20,21,25)(19,22,23,24)(28,33)(30,31);(27,30)(28,33)(31,32)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921915, #16947074, #16947079, …
maximal subgroup of	C₁₇×#7430, C₁₇×#12208, C₁₇×#12209, …
maximal normal subgroup of	C₁₇×#7430, C₁₇×#12208, C₁₇×#12209, …
maximal quotient of	C₁₇×#10340, C₁₇×#10343, C₁₇×#10344, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 759);