C₁₇×#3249 #14526255

order	2176
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#3249

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 188 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 188 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)(19,22)(20,24)(26,27,30,33)(28,34,36,41)(29,37,39,32)(31,38,40,35);(18,19)(20,23)(21,22)(24,25);(19,22)(23,25)(26,28,30,36)(27,31,33,40)(29,38,39,35)(32,41,37,34);(18,20,21,24)(19,23,22,25)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16935278, #16935283, #16936415, …
maximal subgroup of	C₁₇×#10030, C₁₇×#10031, C₁₇×#10195, …
maximal normal subgroup of	C₁₇×#10030, C₁₇×#10031, C₁₇×#10195, …
maximal quotient of	C₁₇×#21885, C₁₇×#21961, C₁₇×#22113, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1981);