C₁₇×#2804 #14525810

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2804

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

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

normal subgroups only

This group has 480 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) = 1088

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16923082, #16923140, #16923320, …
maximal subgroup of	C₁₇×#7745, C₁₇×#7755, C₁₇×#7782, …
maximal normal subgroup of	C₁₇×#7745, C₁₇×#7755, C₁₇×#7782, …
maximal quotient of	C₁₇×#14440, C₁₇×#14457, C₁₇×#14471, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1536);