C₁₇×#2029 #14525035

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2029

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁴×C₁₇ ◁ G

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

normal subgroups only

This group has 466 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) = 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)(18,19,21,24)(20,26,27,23)(22,25,29,31)(28,32,33,30);(18,20,21,27)(19,23,24,26)(22,28,29,33)(25,30,31,32);(23,30)(26,32)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921903, #16947040, #16947045, …
maximal subgroup of	C₁₇×#7426, C₁₇×#12202, C₁₇×#12203, …
maximal normal subgroup of	C₁₇×#7426, C₁₇×#12202, C₁₇×#12203, …
maximal quotient of	C₁₇×#10340, C₁₇×#10341, C₁₇×#10344, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 761);