C₁₇×#1611 #14524617

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

Aliases

direct product

C₁₇×#1611

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂³×C₁₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

210 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 41
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947078, #16947085, #16947092, …
maximal subgroup of	C₁₇×#12209, C₁₇×#12210, C₁₇×#12211, …
maximal normal subgroup of	C₁₇×#12209, C₁₇×#12210, C₁₇×#12211, …
maximal quotient of	C₁₇×#7794, C₁₇×#7798, C₁₇×#7807, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 343);