C₁₇×#1984 #14524990

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1984

Subgroups

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

292 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 160 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) = 2176

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)(19,21)(22,23)(24,28)(25,26)(27,29)(30,31,33,36,34,32,35,37);(18,19,20,21)(23,26)(27,28)(30,32,33,37,34,31,35,36);(22,24,25,29)(23,27,26,28)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16920949, #16921136, #16921328, …
maximal subgroup of	C₁₇×#7057, C₁₇×#7128, C₁₇×#7206, …
maximal normal subgroup of	C₁₇×#7057, C₁₇×#7128, C₁₇×#7206, …
maximal quotient of	C₁₇×#9864, C₁₇×#9865, C₁₇×#9866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 716);