C₁₇×#2003 #14525009

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2003

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂×C₁₇×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

382 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 92 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)(24,28)(25,27)(26,30)(29,33)(31,36)(32,37)(34,35);(23,27)(25,33)(28,36)(29,30)(31,34)(35,37);(19,21)(22,24,26,32)(23,28,30,37)(25,34,33,31)(27,35,29,36)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2003, #17061230, #17061241, …
maximal subgroup of	C₂×C₁₇×#2003, C₁₇×#23399, C₁₇×#23400, …
maximal normal subgroup of	C₂×C₁₇×#2003, C₁₇×#23399, C₁₇×#23400, …
maximal quotient of	C₁₇×#9915, C₁₇×#9921, C₁₇×#9923, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 735);