C₁₇×#1801 #14524807

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1801

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

272 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 124 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) = 37
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921416, #16921639, #16925879, …
maximal subgroup of	C₁₇×#7238, C₁₇×#7323, C₁₇×#8354, …
maximal normal subgroup of	C₁₇×#7238, C₁₇×#7323, C₁₇×#8354, …
maximal quotient of	C₁₇×#8558, C₁₇×#8560, C₁₇×#8562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 533);