C₁₇×#3160 #14526166

order	2176
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#3160

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂²×D₄
prime radical	C₂³×C₁₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

356 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 1088

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(26,27)(28,35)(29,33)(30,39)(31,34)(32,37)(36,40)(38,41);(18,20,21,25)(19,22,23,24);(26,28,30,37,31,38,29,36)(27,32,33,35,34,40,39,41);(26,29,31,30)(27,33,34,39)(28,36,38,37)(32,35,40,41)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16929641, #16933666, #16933683, …
maximal subgroup of	C₁₇×#9068, C₁₇×#9749, C₁₇×#9752, …
maximal normal subgroup of	C₁₇×#9068, C₁₇×#9749, C₁₇×#9752, …
maximal quotient of	C₁₇×#20797, C₁₇×#21151, C₁₇×#21318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1892);