C₁₇×#1594 #14524600

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

Aliases

direct product

C₁₇×#1594

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	C₄×D₄
prime radical	C₂×D₈×C₁₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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)(18,19,21,23)(20,22,25,24)(26,27,30,28,29,31,33,32);(19,22)(20,25)(23,24)(27,31)(28,32);(19,23)(22,24)(26,28,30,31,29,32,33,27)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16946280, #16946294, #16946337, …
maximal subgroup of	C₁₇×#12078, C₁₇×#12080, C₁₇×#12087, …
maximal normal subgroup of	C₁₇×#12078, C₁₇×#12080, C₁₇×#12087, …
maximal quotient of	C₁₇×#8208, C₁₇×#8287, C₁₇×#8849, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 326);