Finite Group Databasebeta

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C5×#23900 #11946620

order1280
nilpotency class3
isoclinismisoclinic class of #23900
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C28

Aliases

direct productC5×#23900

Subgroups

subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

3520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 4 generators on 17 points:

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

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofAGL(1,𝔽5)×#23900, #72242884, #72242902, …
maximal subgroup ofD5×#23900, #72242902, C5×#144366, …
maximal normal subgroup ofD5×#23900, #72242902, C5×#144366, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16888);