C₁₇×#1972 #14524978

order	2176
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#1972

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₂²×D₈×C₁₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

376 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921085, #16951475, #16951580, …
maximal subgroup of	C₁₇×#7110, C₁₇×#13025, C₁₇×#13040, …
maximal normal subgroup of	C₁₇×#7110, C₁₇×#13025, C₁₇×#13040, …
maximal quotient of	C₁₇×#9659, C₁₇×#9665, C₁₇×#9721, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 704);