C₁₇×#2063 #14525069

order	2176
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2063

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ G

228 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 544

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#2063, #17062868, #17062877, …
maximal subgroup of	C₂×C₁₇×#2063, C₁₇×#23601, C₁₇×#23602, …
maximal normal subgroup of	C₂×C₁₇×#2063, C₁₇×#23601, C₁₇×#23602, …
maximal quotient of	C₁₇×#10587, C₁₇×#10589, C₁₇×#10591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 795);