C₁₇×#1632 #14524638

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1632

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₇
prime radical	C₂×D₄×C₁₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

214 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 72 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 — 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)(26,27,30,33)(28,34,36,41)(29,37,39,32)(31,38,40,35);(20,24)(22,25)(26,28,30,36)(27,31,33,40)(29,38,39,35)(32,41,37,34);(18,19)(20,25)(21,23)(22,24)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1632, #17009975, #17010312, …
maximal subgroup of	C₂×C₁₇×#1632, C₁₇×#18480, C₁₇×#18519, …
maximal normal subgroup of	C₂×C₁₇×#1632, C₁₇×#18480, C₁₇×#18519, …
maximal quotient of	C₁₇×#7756, C₁₇×#7761, C₁₇×#7782, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 364);