C₁₇×#1288 #14524294

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1288

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#95
commutator	C₂×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₇
prime radical	C₂³×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 152 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 — 2 generators on 41 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1288, #16924166, #16924170, …
maximal subgroup of	C₂×C₁₇×#1288, C₁₇×#7972, C₁₇×#7973, …
maximal normal subgroup of	C₂×C₁₇×#1288, C₁₇×#7972, C₁₇×#7973, …
maximal quotient of	C₁₇×#7019, C₁₇×#7023, C₁₇×#7024, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 20);