C₁₇×#2809 #14525815

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#2809

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

368 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 192 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 — 4 generators on 41 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16923074, #16923167, #16923243, …
maximal subgroup of	C₁₇×#7743, C₁₇×#7760, C₁₇×#7771, …
maximal normal subgroup of	C₁₇×#7743, C₁₇×#7760, C₁₇×#7771, …
maximal quotient of	C₁₇×#14446, C₁₇×#14464, C₁₇×#14467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1541);