C₁₇×#1870 #14524876

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1870

Subgroups

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

408 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 136 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)(26,27,30,32,29,28,31,33);(18,19,20,21)(26,28,30,33,29,27,31,32);(23,25)(27,28)(32,33)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921533, #16921540, #16921629, …
maximal subgroup of	C₁₇×#7282, C₁₇×#7285, C₁₇×#7320, …
maximal normal subgroup of	C₁₇×#7282, C₁₇×#7285, C₁₇×#7320, …
maximal quotient of	C₁₇×#8941, C₁₇×#8942, C₁₇×#8943, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 602);