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C5×#26393 #11949113

order1280
nilpotency class3
isoclinismisoclinic class of #23860
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#26393

Subgroups

subgroupG/H
center, socle, prime radicalC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C4⋊C4 ◁ G

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1280

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 19381);