C₅×#14350 #11937070

order	1280
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅×#14350

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂⁴	C₂⁴×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

1118 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 462 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) = 1280

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

320 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 7338);