C₁₇×#1704 #14524710

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#1704

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 140 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) = 2176

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

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1704, #17017009, #17017043, …
maximal subgroup of	C₂×C₁₇×#1704, C₁₇×#19155, C₁₇×#19158, …
maximal normal subgroup of	C₂×C₁₇×#1704, C₁₇×#19155, C₁₇×#19158, …
maximal quotient of	C₁₇×#8657, C₁₇×#9224, C₁₇×#9228, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 436);