C₁₇×#2647 #14525653

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#2647

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

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

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 200 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)(19,20)(23,24)(26,27)(28,31)(29,32)(30,33)(34,35,38,36)(37,40,41,39);(18,19,22,20)(21,23,25,24)(26,28)(27,29)(30,32)(31,33)(34,36,38,35)(37,39,41,40);(18,20,22,19)(21,23,25,24)(26,28)(27,31)(29,33)(30,32)(34,37,38,41)(35,39,36,40);(18,21,22,25)(19,23,20,24)(26,29,30,31)(27,32,33,28)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17134086, #17134097, #17134110, …
maximal subgroup of	C₁₇×#29133, C₁₇×#29134, C₁₇×#29135, …
maximal normal subgroup of	C₁₇×#29133, C₁₇×#29134, C₁₇×#29135, …
maximal quotient of	C₁₇×#14266, C₁₇×#14276, C₁₇×#14277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1379);