C₁₇×#3140 #14526146

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#3140

Subgroups

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

400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 544

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)(20,23)(21,22)(24,25)(26,27)(28,36)(29,32)(30,40)(31,35)(33,38)(34,37)(39,41);(19,22)(23,25)(26,28,37,39,31,38,30,29)(27,32,40,33,35,41,34,36);(18,20,21,24)(19,23,22,25)(26,29,30,38,31,39,37,28)(27,33,34,32,35,36,40,41);(28,38)(29,39)(32,41)(33,36)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931944, #16935226, #16935240, …
maximal subgroup of	C₁₇×#9439, C₁₇×#10022, C₁₇×#10024, …
maximal normal subgroup of	C₁₇×#9439, C₁₇×#10022, C₁₇×#10024, …
maximal quotient of	C₁₇×#20765, C₁₇×#21094, C₁₇×#21095, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1872);