C₁₇×#3189 #14526195

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

Aliases

direct product

C₁₇×#3189

Subgroups

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

416 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 416 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) = 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)(20,24)(21,23)(22,25)(26,27,30,33)(28,34,36,41)(29,37,39,32)(31,38,40,35);(18,20)(19,22)(21,25)(23,24);(20,25)(22,24)(26,28,30,36)(27,31,33,40)(29,38,39,35)(32,41,37,34);(19,23)(22,24)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16930892, #16934805, #16934819, …
maximal subgroup of	C₁₇×#9276, C₁₇×#9955, C₁₇×#9957, …
maximal normal subgroup of	C₁₇×#9276, C₁₇×#9955, C₁₇×#9957, …
maximal quotient of	C₁₇×#21759, C₁₇×#21940, C₁₇×#22044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1921);