C₁₇×#1443 #14524449

order	2176
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#1443

Subgroups

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

476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 2176

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

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1443, #16956024, #16956048, …
maximal subgroup of	C₂×C₁₇×#1443, C₁₇×#13842, C₁₇×#13846, …
maximal normal subgroup of	C₂×C₁₇×#1443, C₁₇×#13842, C₁₇×#13846, …
maximal quotient of	C₁₇×#7556, C₁₇×#11298, C₁₇×#11299, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 175);