Finite Group Databasebeta

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C5×#23996 #11946716

order1280
nilpotency class3
isoclinismisoclinic class of #23996
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#23996

Subgroups

subgroupG/H
center, socleC2×C5#2404
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C24×C5 ◁ G

1396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD5×#23996, #72253568, AGL(1,𝔽5)×#23996, …
maximal subgroup ofC5×#6499874, D5×#23996, #72253568
maximal normal subgroup ofC5×#6499874, D5×#23996, #72253568

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16984);