C₁₇×#2080 #14525086

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2080

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂×C₁₇	#397
prime radical	C₂×#41×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

190 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,31,41)(21,25)(22,26)(23,27)(24,30,38,35)(29,44,32,43)(33,39)(34,40)(36,42)(37,46,48,45)(47,49);(18,20)(19,24)(21,32)(22,35)(23,31)(25,37)(26,41)(27,38)(28,42)(29,34)(30,36)(33,45)(39,44)(40,48)(43,49)(46,47);(18,21,22,33,23,34,36,47)(19,25,26,39,27,40,42,49)(20,29,30,45,31,32,35,46)(24,37,28,43,38,48,41,44)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2080, #17063249, #17065205, …
maximal subgroup of	C₂×C₁₇×#2080, C₁₇×#23649, C₁₇×#23833, …
maximal normal subgroup of	C₂×C₁₇×#2080, C₁₇×#23649, C₁₇×#23833, …
maximal quotient of	C₁₇×#10627, C₁₇×#10628, C₁₇×#10629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 812);