C₁₇×#1664 #14524670

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1664

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₂×D₄×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

184 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 1088

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

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1664, #17015500, #17015527, …
maximal subgroup of	C₂×C₁₇×#1664, C₁₇×#18987, C₁₇×#18990, …
maximal normal subgroup of	C₂×C₁₇×#1664, C₁₇×#18987, C₁₇×#18990, …
maximal quotient of	C₁₇×#7764, C₁₇×#7765, C₁₇×#7766, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 396);