C₁₇×#1615 #14524621

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1615

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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)(18,19,25,35)(20,29,40,49)(21,23,28,24)(22,34,41,45)(26,42,48,31)(27,38,37,39)(30,46,43,36)(32,44,33,47);(18,20)(19,26)(21,30)(22,36)(23,33)(24,32)(25,40)(27,44)(28,43)(29,34)(31,39)(35,48)(37,47)(38,42)(41,46)(45,49);(18,21,24,19)(20,30,32,26)(22,37,39,45)(23,35,25,28)(27,38,34,41)(29,46,44,42)(31,49,36,47)(33,48,40,43)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1615, #17006484, #17006642, …
maximal subgroup of	C₂×C₁₇×#1615, C₁₇×#18107, C₁₇×#18127, …
maximal normal subgroup of	C₂×C₁₇×#1615, C₁₇×#18107, C₁₇×#18127, …
maximal quotient of	C₁₇×#7787, C₁₇×#7788, C₁₇×#7798, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 347);