C₁₇×#1937 #14524943

order	2176
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1937

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	C₄×D₄
prime radical	C₂×#41×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

230 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,26,30,27,31,25,28)(24,32,34,29,35,36,33,37);(23,28,31,30)(29,32,37,36);(19,21)(22,24,25,33,27,35,26,34)(23,29,30,36,31,37,28,32)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1937, #17037070, #17037079, …
maximal subgroup of	C₂×C₁₇×#1937, C₁₇×#21098, C₁₇×#21099, …
maximal normal subgroup of	C₂×C₁₇×#1937, C₁₇×#21098, C₁₇×#21099, …
maximal quotient of	C₁₇×#9553, C₁₇×#9554, C₁₇×#9559, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 669);