C₁₇×#1542 #14524548

order	2176
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1542

Subgroups

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

212 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 108 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)(18,19,22,25,23,20,21,24)(26,27,30,35,31,34,29,33)(28,36,37,41,38,32,39,40);(18,20,23,19)(21,24,22,25)(26,28)(27,32)(29,37)(30,39)(31,38)(33,40)(34,36)(35,41);(26,29,31,30)(27,33,34,35)(28,37,38,39)(32,40,36,41)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16925401, #16925415, #16925429, …
maximal subgroup of	C₁₇×#8252, C₁₇×#8254, C₁₇×#8256, …
maximal normal subgroup of	C₁₇×#8252, C₁₇×#8254, C₁₇×#8256, …
maximal quotient of	C₁₇×#7562, C₁₇×#7566, C₁₇×#7644, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 274);