C₁₇×#2009 #14525015

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2008
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2009

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#392
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 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)(20,30)(21,34)(22,28)(23,27)(24,29)(25,32)(26,36)(31,39)(33,44)(35,43)(37,42)(38,40)(41,47)(45,46)(48,49);(18,20)(19,25)(21,31)(22,38)(23,32)(24,33)(26,41)(27,44)(28,30)(29,40)(34,45)(35,48)(36,46)(37,47)(39,43)(42,49);(18,21,24,37)(19,26,29,43)(20,31,33,47)(22,36,23,35)(25,39,40,41)(27,34,28,42)(30,45,44,49)(32,48,38,46)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2009, #17061331, #17065624, …
maximal subgroup of	C₂×C₁₇×#2009, C₁₇×#23412, C₁₇×#23873, …
maximal normal subgroup of	C₂×C₁₇×#2009, C₁₇×#23412, C₁₇×#23873, …
maximal quotient of	C₁₇×#9931, C₁₇×#9933, C₁₇×#9935, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 741);