C₁₇×#1718 #14524724

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#1718

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 164 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) = 2176

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)(18,19,22,25)(20,26,27,33)(21,29,30,24)(23,31,32,28)(34,35)(36,42)(37,39)(38,46)(40,44)(41,45)(43,48)(47,49);(18,20,21,28,22,27,30,31)(19,23,24,26,25,32,29,33)(35,39)(40,47)(41,46)(42,48);(20,27)(23,32)(26,33)(28,31)(34,36,38,44,37,43,45,49)(35,40,41,42,39,47,46,48)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1718, #17022099, #17022149, …
maximal subgroup of	C₂×C₁₇×#1718, C₁₇×#19613, C₁₇×#19620, …
maximal normal subgroup of	C₂×C₁₇×#1718, C₁₇×#19613, C₁₇×#19620, …
maximal quotient of	C₁₇×#8821, C₁₇×#9826, C₁₇×#9828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 450);