C₁₇×#1662 #14524668

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

Aliases

direct product

C₁₇×#1662

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₁₇×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 196 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)(34,35,38,41)(36,42,44,49)(37,45,47,40)(39,46,48,43);(18,20)(19,24)(21,31)(22,29)(23,30)(25,33)(26,28)(27,32)(34,36,38,44)(35,39,41,48)(37,46,47,43)(40,49,45,42);(18,20)(19,24)(21,29)(22,31)(23,30)(25,28)(26,33)(27,32)(37,47)(40,45)(42,49)(43,46)

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922170, D₁₇×#1662, #17015502, …
maximal subgroup of	C₁₇×#7525, C₂×C₁₇×#1662, C₁₇×#18987, …
maximal normal subgroup of	C₁₇×#7525, C₂×C₁₇×#1662, C₁₇×#18987, …
maximal quotient of	C₁₇×#7762, C₁₇×#7769, C₁₇×#7773, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 394);