C₅×#23896 #11946616

order	1280
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₅×#23896

Subgroups

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

1764 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1764 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)(8,12)(9,13)(10,14)(11,15)(16,22)(17,23)(18,24)(19,32)(20,27)(21,28)(25,30)(26,33)(29,36)(31,35)(34,37);(6,8,11,18)(7,12,15,24)(9,16,20,30)(10,17,21,31)(13,25,27,22)(14,23,28,35)(19,29,33,37)(26,36,32,34);(6,9)(7,13)(8,16)(10,19)(11,20)(12,22)(14,26)(15,27)(17,29)(18,30)(21,33)(23,34)(24,25)(28,32)(31,37)(35,36);(6,10)(7,14)(8,17)(9,19)(11,21)(12,23)(13,26)(15,28)(16,29)(18,31)(20,33)(22,34)(24,35)(25,36)(27,32)(30,37)

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, 16884);