C₁₇×#2228 #14525234

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#2228

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

136 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 64 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)(18,19,21,23)(20,24,25,22)(26,27,28,31)(29,32,35,39)(30,38,36,34)(33,41,40,37);(18,20,21,25)(19,22,23,24)(27,31)(32,39)(33,40)(34,38);(27,32)(29,37)(30,36)(31,39)(33,34)(35,41)(38,40)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2228, #17188967, #17188977, …
maximal subgroup of	C₂×C₁₇×#2228, C₁₇×#33626, C₁₇×#33627, …
maximal normal subgroup of	C₂×C₁₇×#2228, C₁₇×#33626, C₁₇×#33627, …
maximal quotient of	C₁₇×#12813, C₁₇×#12935, C₁₇×#12937, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 960);