C₁₇×#3185 #14526191

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

Aliases

direct product

C₁₇×#3185

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

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

normal subgroups only

This group has 358 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) = 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)(20,23)(21,22)(24,25)(26,27,30,33)(28,34,35,41)(29,38,36,32)(31,39,40,37);(19,22)(23,25)(28,35)(31,40)(34,41)(37,39);(26,28,36,39,30,35,29,37)(27,31,38,41,33,40,32,34);(18,20,21,24)(19,23,22,25)(28,35)(31,40)(34,41)(37,39)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16931808, #16945176, #17010691, …
maximal subgroup of	C₁₇×#9416, C₁₇×#11838, C₁₇×#18557, …
maximal normal subgroup of	C₁₇×#9416, C₁₇×#11838, C₁₇×#18557, …
maximal quotient of	C₁₇×#20824, C₁₇×#21287, C₁₇×#21409, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1917);