C₁₇×#2983 #14525989

order	2176
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2983

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂³×C₄
prime radical	C₂³×C₁₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

356 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 268 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,23,21,22,24,25)(26,27)(28,34)(29,32)(30,33)(31,36)(35,40)(37,39)(38,41);(26,28,30,36)(27,31,33,34)(29,37,38,35)(32,40,41,39);(19,22)(23,25)(26,29,30,38)(27,32,33,41)(28,35,36,37)(31,39,34,40);(27,33)(31,34)(32,41)(39,40)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16928201, #16928366, #16928994, …
maximal subgroup of	C₁₇×#8838, C₁₇×#8865, C₁₇×#8962, …
maximal normal subgroup of	C₁₇×#8838, C₁₇×#8865, C₁₇×#8962, …
maximal quotient of	C₁₇×#20534, C₁₇×#20536, C₁₇×#20570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1715);