C₁₇×#1935 #14524941

order	2176
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1935

Subgroups

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

248 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 33
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,24)(27,28)(29,30)(32,33);(22,24,25,23)(26,27,29,28,31,33,30,32);(19,21)(26,28,29,33,31,32,30,27)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1935, #17036958, #17036969, …
maximal subgroup of	C₂×C₁₇×#1935, C₁₇×#21086, C₁₇×#21087, …
maximal normal subgroup of	C₂×C₁₇×#1935, C₁₇×#21086, C₁₇×#21087, …
maximal quotient of	C₁₇×#9555, C₁₇×#9559, C₁₇×#9569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 667);