C₁₇×#1616 #14524622

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

Aliases

direct product

C₁₇×#1616

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 246 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)(18,19,21,24)(20,22,25,23)(26,27,30,33)(28,31,35,38)(29,32,36,39)(34,40,41,37);(19,22)(20,25)(23,24)(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	#16946560, #16946567, #16946574, …
maximal subgroup of	C₁₇×#12127, C₁₇×#12128, C₁₇×#12129, …
maximal normal subgroup of	C₁₇×#12127, C₁₇×#12128, C₁₇×#12129, …
maximal quotient of	C₁₇×#7791, C₁₇×#7795, C₁₇×#7808, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 348);