C₅×#13342 #11936062

order	1280
nilpotency class	4
isoclinism	isoclinic class of #13316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅×#13342

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅
prime radical	C₅×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

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

normal subgroups only

This group has 558 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) = 41
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 3 generators on 41 points:

(1,2,3,4,5)(10,11,18,25)(12,20,30,40)(13,31,26,19)(14,22,34,41)(15,21,32,35)(16,24,17,23)(27,38,33,37)(28,39,29,36);(6,7)(8,9)(10,12)(11,19)(13,32)(14,33)(15,26)(16,29)(17,28)(18,30)(20,22)(21,39)(23,38)(24,37)(25,31)(27,34)(35,36)(40,41);(7,9)(10,13)(11,20)(12,14)(15,28)(16,27)(17,33)(18,26)(19,35)(21,31)(22,38)(23,39)(24,36)(25,40)(29,32)(30,34)(37,41)

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6330);