C₁₇×#1682 #14524688

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1682

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₁₇×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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)(28,34)(29,31)(30,38)(32,36)(33,37)(35,41)(39,40);(18,19,23,25,21,24,20,22)(27,31)(32,40)(33,38)(34,41);(26,28,29,35)(27,32,31,40)(30,39,37,36)(33,41,38,34)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1682, #17016731, #17016760, …
maximal subgroup of	C₂×C₁₇×#1682, C₁₇×#19123, C₁₇×#19125, …
maximal normal subgroup of	C₂×C₁₇×#1682, C₁₇×#19123, C₁₇×#19125, …
maximal quotient of	C₁₇×#8649, C₁₇×#9218, C₁₇×#9222, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 414);