C₁₇×#1618 #14524624

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1618

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#538	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 544

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)(19,22)(20,24)(23,25)(26,27,31,34)(28,35,37,40)(29,33,30,38)(32,39,41,36);(18,19)(20,25)(21,23)(22,24)(26,28)(27,32)(29,36)(30,39)(31,37)(33,40)(34,41)(35,38);(20,24)(22,25)(26,29,31,30)(27,33,34,38)(28,36,37,39)(32,40,41,35)

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1618, #17006586, #17006644, …
maximal subgroup of	C₂×C₁₇×#1618, C₁₇×#18121, C₁₇×#18127, …
maximal normal subgroup of	C₂×C₁₇×#1618, C₁₇×#18121, C₁₇×#18127, …
maximal quotient of	C₁₇×#7790, C₁₇×#7793, C₁₇×#7796, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 350);