C₅×#14676 #11937396

order	1280
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅×#14676

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

1182 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 1182 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) = 29
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 7664);