C₁₇×#1805 #14524811

order	2176
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1805

Subgroups

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

292 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 2176

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,24,25)(26,27)(28,34)(29,31)(30,38)(32,36)(33,37)(35,41)(39,40);(18,19,20,21)(27,31)(32,40)(33,38)(34,41);(26,28,29,35)(27,32,31,40)(30,39,37,36)(33,41,38,34)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926299, #16926313, #16926327, …
maximal subgroup of	C₁₇×#8429, C₁₇×#8431, C₁₇×#8433, …
maximal normal subgroup of	C₁₇×#8429, C₁₇×#8431, C₁₇×#8433, …
maximal quotient of	C₁₇×#8566, C₁₇×#8570, C₁₇×#8574, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 537);