C₁₇×#1762 #14524768

order	2176
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#1762

Subgroups

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

388 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 168 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)(22,23,25,24)(27,31)(28,29)(32,33);(19,21)(26,27,29,33,30,32,28,31);(22,24,25,23)(27,32)(31,33)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926204, #16926218, #16930145, …
maximal subgroup of	C₁₇×#8416, C₁₇×#8418, C₁₇×#9163, …
maximal normal subgroup of	C₁₇×#8416, C₁₇×#8418, C₁₇×#9163, …
maximal quotient of	C₁₇×#8170, C₁₇×#8172, C₁₇×#8179, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 494);