C₁₇×#2140 #14525146

order	2176
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#2140

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator	C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂²×D₈×C₁₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

260 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16949597, #16950008, #16950061, …
maximal subgroup of	C₁₇×#12647, C₁₇×#12741, C₁₇×#12750, …
maximal normal subgroup of	C₁₇×#12647, C₁₇×#12741, C₁₇×#12750, …
maximal quotient of	C₁₇×#11593, C₁₇×#11649, C₁₇×#11661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 872);