C₅×#9448 #11932168

order	1280
nilpotency class	3
isoclinism	isoclinic class of #9443
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#9448

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#386
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂²×C₅×D₄	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

486 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 29
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

185 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 2436);