C₅×#14341 #11937061

order	1280
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₅×#14341

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂⁴	C₂⁴×C₅
prime radical	C₂⁶×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

3246 conjugacy classes of subgroups; only the 542 normal subgroups are shown.

normal subgroups only

This group has 3246 conjugacy classes of subgroups — too many to draw. Only its 542 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 — 4 generators on 29 points:

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

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, 7329);