C₁₇×#3166 #14526172

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#3166

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
prime radical	C₂³×C₁₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

348 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 41 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)(26,27,29,31)(28,34,35,41)(30,38,37,33)(32,40,39,36);(18,20,21,25)(19,22,23,24)(27,31)(32,39)(33,38)(34,41);(26,28,30,36,29,35,37,40)(27,32,33,34,31,39,38,41);(28,35)(32,39)(34,41)(36,40)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931949, #16935233, #16935247, …
maximal subgroup of	C₁₇×#9440, C₁₇×#10023, C₁₇×#10025, …
maximal normal subgroup of	C₁₇×#9440, C₁₇×#10023, C₁₇×#10025, …
maximal quotient of	C₁₇×#20801, C₁₇×#21159, C₁₇×#21323, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1898);