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#10624473⋊C2 #13090498

order1458
isoclinismisoclinic class of #10624473⋊C2
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect product#10624473⋊C2

Splittings

Fitting, Sylow#10624473 ⋊ C2
derivedC3×C27 ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC3×C27C2×C9
FrattiniC32×C9C3×D3
Fitting#10624473C2
socleC3#92158
prime radicalC3⋊(D27⋊C3)C3
cosocleC3×C27⋊C3C2×C3
LCSG ▷ C3×C27
UCSC1

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 81

Polycyclic presentation:

2,3^6|b^3=e,c^3=f,d^3=g^2,f^3=g^2,c^a=c^2f^2g,d^a=d^2g,f^a=f^2g,g^a=g^2,c^b=cd,d^b=dg,f^b=fg^2,e^c=eg

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221840, #72221841, #72221842, …
maximal normal subgroup of#72221840, #72221841, #72221842, …
maximal quotient ofC2×#10624473⋊C2

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 572);