C₁₇×#2001 #14525007

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2001

Subgroups

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

392 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 112 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)(18,19)(20,21)(26,27,30,33)(28,34,36,41)(29,37,39,32)(31,38,40,35);(22,23)(24,25)(26,28,30,36)(27,31,33,40)(29,38,39,35)(32,41,37,34);(19,21)(23,25)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921003, #16921027, #16946437, …
maximal subgroup of	C₁₇×#7078, C₁₇×#7086, C₁₇×#12105, …
maximal normal subgroup of	C₁₇×#7078, C₁₇×#7086, C₁₇×#12105, …
maximal quotient of	C₁₇×#9924, C₁₇×#9925, C₁₇×#9928, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 733);