C₁₇×#1977 #14524983

order	2176
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#1977

Subgroups

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

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

normal subgroups only

This group has 296 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) = 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)(19,21)(22,23,27,31,28,30,26,24)(25,33,35,37,36,32,34,29);(18,19,20,21)(22,24,27,30,28,31,26,23)(25,32,35,37,36,33,34,29);(22,25,26,34,28,36,27,35)(23,29,31,33,30,37,24,32)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1977, #17038326, #17038334, …
maximal subgroup of	C₂×C₁₇×#1977, C₁₇×#21248, C₁₇×#21249, …
maximal normal subgroup of	C₂×C₁₇×#1977, C₁₇×#21248, C₁₇×#21249, …
maximal quotient of	C₁₇×#9667, C₁₇×#9672, C₁₇×#9723, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 709);