C₁₇×#2801 #14525807

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

Aliases

direct product

C₁₇×#2801

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

420 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 176 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)(26,27,29,31)(28,32,33,30)(35,36)(39,40);(19,22)(23,25)(34,35,38,36)(37,40,41,39);(18,19,21,22)(20,23,24,25)(26,27)(28,30)(29,31)(32,33)(34,36,38,35)(37,40,41,39);(18,20,21,24)(19,23,22,25)(26,28,29,33)(27,30,31,32)(34,37,38,41)(35,39,36,40)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#17242348, #17242453, #17244100, …
maximal subgroup of	C₁₇×#36766, C₁₇×#36769, C₁₇×#36826, …
maximal normal subgroup of	C₁₇×#36766, C₁₇×#36769, C₁₇×#36826, …
maximal quotient of	C₁₇×#14434, C₁₇×#14459, C₁₇×#14504, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1533);