C₁₇×#1461 #14524467

order	2176
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1461

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²⋊C₄
commutator	C₂²	C₂²×C₈×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

248 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 124 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 — 3 generators on 41 points:

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

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921327, #16921544, #16924890, …
maximal subgroup of	C₁₇×#7206, C₁₇×#7286, C₈×C₁₇×#101, …
maximal normal subgroup of	C₁₇×#7206, C₁₇×#7286, C₈×C₁₇×#101, …
maximal quotient of	C₁₇×#7568, C₁₇×#7570, C₁₇×#7585, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 193);