C₁₇×#1998 #14525004

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1998

Subgroups

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

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

normal subgroups only

This group has 228 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)(20,24)(21,22)(23,25)(26,27,30,33,29,32,34,40)(28,31,36,39,35,38,37,41);(19,22)(23,24)(26,28,34,36,29,35,30,37)(27,31,33,41,32,38,40,39);(18,20,21,25)(19,23,22,24)(27,32)(31,38)(33,40)(39,41)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926635, #16926642, #16938289, …
maximal subgroup of	C₁₇×#8485, C₁₇×#8486, C₁₇×#10497, …
maximal normal subgroup of	C₁₇×#8485, C₁₇×#8486, C₁₇×#10497, …
maximal quotient of	C₁₇×#9880, C₁₇×#9881, C₁₇×#9892, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 730);