Finite Group Databasebeta

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#10617014⋊C3 #14512345

order1920
isoclinismisoclinic class of #10617014⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#10617014⋊C3
unambiguous semidirect product((#564⋊C3)⋊C5)⋊C2

Splittings

Fitting#564 ⋊ C3×D5
derived#564⋊C5 ⋊ C2×C3
Hall#10617014 ⋊ C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#564⋊C5C2×C3
Frattini, socleC22((C24⋊C5)⋊C2)⋊C3
Fitting#564C3×D5
LCSG ▷ #564⋊C5
UCSC1

49 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 64

Polycyclic presentation:

2,3,5,2^6|d^2=i,e^2=h,f^2=hi,g^2=i,c^a=c^4,d^a=dei,e^a=eh,f^a=fgh,g^a=gi,d^b=dfghi,e^b=eghi,f^b=de,g^b=e,h^b=hi,i^b=h,d^c=de,e^c=ef,f^c=deghi,g^c=defg,e^d=eh,f^d=fhi,g^d=ghi,f^e=fhi,g^f=gi

Conjugacy classes & character table

18 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72272633

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238043);