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C24⋊(C24⋊C5) #13046088

order1280
isoclinismisoclinic class of C24⋊(C24⋊C5)
automorphism?
homologyAbelianization (H1) = C5 · Schur multiplier (H2) = C28

Aliases

unambiguous semidirect productC24⋊(C24⋊C5)

Splittings

Fitting, socle, derived, SylowC28 ⋊ C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC28C5
LCSG ▷ C28
UCSC1

83474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20

Polycyclic presentation:

5,2^8|b^a=hi,c^a=bcefhi,d^a=egh,e^a=bcefh,f^a=bi,g^a=cdi,h^a=bcdei,i^a=bdeh

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

derived subgroup of#72227520, #72239935, C2×#72227520
maximal subgroup of#72209701, C2×C24⋊(C24⋊C5), #72218551, …
maximal normal subgroup of#72209701, C2×C24⋊(C24⋊C5), #72218551, …
maximal quotient of#72210028, C2×C24⋊(C24⋊C5), #72211295

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116356);