C₁₇×#3414 #14526420

order	2176
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#3414

Subgroups

	subgroup	G/H
center	C₄×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₁₇
socle	C₂×C₁₇	C₂²×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

364 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 180 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 — 4 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29)(21,27)(22,34)(23,38)(24,26)(25,31)(28,36)(30,46)(32,45)(33,43)(35,41)(37,48)(39,44)(40,47)(42,49);(18,20)(19,25)(21,30)(22,35)(23,39)(24,32)(26,40)(27,41)(28,44)(29,34)(31,36)(33,47)(37,49)(38,42)(43,46)(45,48);(19,26)(25,40)(27,38)(28,43)(29,45)(34,48)(41,42)(44,46);(18,21,24,23)(19,27,26,38)(20,30,32,39)(22,33,37,36)(25,41,40,42)(28,34,43,48)(29,46,45,44)(31,35,47,49)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16951446, #16951467, #16951488, …
maximal subgroup of	C₁₇×#13021, C₁₇×#13024, C₁₇×#13027, …
maximal normal subgroup of	C₁₇×#13021, C₁₇×#13024, C₁₇×#13027, …
maximal quotient of	C₁₇×#33380, C₁₇×#33409, C₁₇×#33451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2146);