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C2×C5×#2370 #11956864

order1280
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C28

Aliases

direct productC2×C5×#2370

Subgroups

subgroupG/H
center, socle, prime radicalC24×C5C24
commutatorC22C24×C4×C5
Frattini, cosocleC23C25×C5
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

2510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 1280

A minimal faithful permutation representation — 5 generators on 27 points:

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

Conjugacy classes & character table

500 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 27132);