C₁₇×#1768 #14524774

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1768

Subgroups

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

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

normal subgroups only

This group has 260 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 41 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)(26,27)(28,31)(29,33)(30,32)(34,38)(35,37)(36,39)(40,41);(19,21)(26,28,29,34,30,35,36,40)(27,31,33,38,32,37,39,41);(22,24,25,23)(27,32)(31,37)(33,39)(38,41)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1768, #17032211, #17032218, …
maximal subgroup of	C₂×C₁₇×#1768, C₄×C₁₇×#424, C₁₇×#20427, …
maximal normal subgroup of	C₂×C₁₇×#1768, C₄×C₁₇×#424, C₁₇×#20427, …
maximal quotient of	C₁₇×#8264, C₁₇×#8265, C₁₇×#8270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 500);