C₁₇×#1913 #14524919

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1913

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#386
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₁₇×#534	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂⁴×C₁₇ ◁ G

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

normal subgroups only

This group has 380 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)(20,23,27,31)(21,28,29,24)(22,25)(26,30)(32,33);(18,20)(19,23,25,31)(21,26)(22,27)(24,30,28,33)(29,32);(18,21)(19,24)(20,26)(22,29)(23,30)(25,28)(27,32)(31,33)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16950084, #16950091, #16950167, …
maximal subgroup of	C₁₇×#12753, C₁₇×#12754, C₁₇×#12767, …
maximal normal subgroup of	C₁₇×#12753, C₁₇×#12754, C₁₇×#12767, …
maximal quotient of	C₁₇×#9107, C₁₇×#9108, C₁₇×#9109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 645);