C₁₇×#2209 #14525215

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2209

Subgroups

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

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

normal subgroups only

This group has 154 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) = 53
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,27,31)(24,32,35,51)(25,36,40,50)(26,41,38,30)(28,43,45,33)(29,46,48,39)(34,52,42,47)(37,49,53,44);(18,19,20,21);(22,24,27,35)(23,28,31,45)(25,37,40,53)(26,42,38,34)(29,47,48,52)(30,49,41,44)(32,50,51,36)(33,46,43,39)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947782, #16947789, #16947824, …
maximal subgroup of	C₁₇×#12321, C₁₇×#12322, C₁₇×#12327, …
maximal normal subgroup of	C₁₇×#12321, C₁₇×#12322, C₁₇×#12327, …
maximal quotient of	C₁₇×#12421, C₁₇×#12427, C₁₇×#12448, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 941);