C₁₇×#1450 #14524456

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₇×#1450

Subgroups

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

212 conjugacy classes of subgroups.

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

1360 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#16921160, #16921163, #16921191, …
maximal subgroup of	C₁₇×#7140, C₁₇×#7141, C₁₇×#7153, …
maximal normal subgroup of	C₁₇×#7140, C₁₇×#7141, C₁₇×#7153, …
maximal quotient of	C₁₇×#7841, C₁₇×#7849, C₁₇×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 182);

C17×#1450 #14524456