C₁₇×#1851 #14524857

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1851

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂³
commutator	C₂³	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂³×C₁₇	C₂²×C₄
prime radical	C₂⁴×C₁₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

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

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 1088

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)(24,25)(26,27,30,28,29,31,33,32);(19,21)(26,28,30,31,29,32,33,27);(23,25)(27,31)(28,32)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16920970, #16928427, #16928434, …
maximal subgroup of	C₁₇×#7067, C₁₇×#8874, C₁₇×#8875, …
maximal normal subgroup of	C₁₇×#7067, C₁₇×#8874, C₁₇×#8875, …
maximal quotient of	C₁₇×#8832, C₁₇×#8833, C₁₇×#8834, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 583);