C₁₇×#1645 #14524651

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1645

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

200 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 2176

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)(28,34,35,41)(29,37,38,32)(31,39,40,36);(18,19,21,23)(20,25,24,22)(29,38)(32,37)(34,41)(36,39);(26,28,30,35)(27,31,33,40)(29,39,38,36)(32,41,37,34)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1645, #17010262, #17010307, …
maximal subgroup of	C₂×C₁₇×#1645, C₁₇×#18515, C₁₇×#18518, …
maximal normal subgroup of	C₂×C₁₇×#1645, C₁₇×#18515, C₁₇×#18518, …
maximal quotient of	C₁₇×#7759, C₁₇×#7761, C₁₇×#7766, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 377);