C₁₇×#1834 #14524840

order	2176
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1834

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 152 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) = 2176

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)(18,19,20,21)(22,23)(24,27)(25,26)(28,29)(31,36)(32,37)(33,34);(23,26)(27,29)(30,31,34,32,35,37,33,36);(22,24,25,28)(23,27,26,29)(30,32,33,31,35,36,34,37)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921360, #16921375, #16927385, …
maximal subgroup of	C₁₇×#7217, C₁₇×#7222, C₁₇×#8646, …
maximal normal subgroup of	C₁₇×#7217, C₁₇×#7222, C₁₇×#8646, …
maximal quotient of	C₁₇×#8784, C₁₇×#8787, C₁₇×#8790, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 566);