C₅×#23899 #11946619

order	1280
nilpotency class	3
isoclinism	isoclinic class of #23897
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₅×#23899

Subgroups

	subgroup	G/H
center, socle	C₂×C₅	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ G

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 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) = 37
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16887);