C₁₇×#2099 #14525105

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2099

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

214 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 100 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)(18,19,22,24)(20,25,21,23)(26,27)(28,30)(29,31)(32,33);(18,20,22,21)(19,23,24,25)(26,28,29,32)(27,30,31,33)(34,35)(36,38)(37,40)(39,41);(18,21,22,20)(19,23,24,25)(27,31)(30,33)(35,38)(36,41)(39,40)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16923352, #16923359, #16923380, …
maximal subgroup of	C₁₇×#7787, C₁₇×#7788, C₁₇×#7791, …
maximal normal subgroup of	C₁₇×#7787, C₁₇×#7788, C₁₇×#7791, …
maximal quotient of	C₁₇×#10687, C₁₇×#11207, C₁₇×#11267, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 831);