C₁₇×#1571 #14524577

order	2176
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1571

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 168 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)(19,22)(20,23)(24,25)(26,27,29,32,30,33,36,39)(28,31,35,38,34,37,40,41);(18,19,23,25,21,24,20,22)(26,28)(27,31)(29,35)(30,34)(32,38)(33,37)(36,40)(39,41);(28,34)(31,37)(35,40)(38,41)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928342, #16928352, #16928453, …
maximal subgroup of	C₁₇×#8861, C₁₇×#8863, C₁₇×#8878, …
maximal normal subgroup of	C₁₇×#8861, C₁₇×#8863, C₁₇×#8878, …
maximal quotient of	C₁₇×#7877, C₁₇×#8278, C₁₇×#8599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 303);