C₁₇×#1906 #14524912

order	2176
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1906

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#121
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂×C₁₇	#386
prime radical	C₁₇×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 332 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)(20,23,27,33)(21,26)(22,25)(24,28,32,29)(30,31);(18,20)(19,23,25,33)(21,29)(22,27)(24,31,32,26)(28,30);(18,20)(19,24)(21,29)(22,27)(23,31)(25,32)(26,33)(28,30)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1906, #17036235, #17041260, …
maximal subgroup of	C₂×C₁₇×#1906, C₁₇×#21000, C₁₇×#21558, …
maximal normal subgroup of	C₂×C₁₇×#1906, C₁₇×#21000, C₁₇×#21558, …
maximal quotient of	C₁₇×#9095, C₁₇×#9096, C₁₇×#9097, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 638);