Finite Group Databasebeta

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C53×D255 #41028419

order27030
automorphism?
homologyAbelianization (H1) = C2×C53 · Schur multiplier (H2) = C1

Aliases

direct productC53×D255
unambiguous semidirect productC3⋊(C53×D85)
unambiguous semidirect productC5⋊(C53×D51)
unambiguous semidirect productC17⋊(D15×C53)

Splittings

Fitting, socle, HallC3×C5×C17×C53 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C53
HallC5×C17×C53 ⋊ D3
HallC3×C17×C53 ⋊ D5
HallC17×C53 ⋊ D15
HallC3×C5×C53 ⋊ D17
HallC5×C53 ⋊ D51
HallC3×C53 ⋊ D85
HallC5×C17 ⋊ D3×C53
HallC3×C17 ⋊ D5×C53
SylowC17 ⋊ D15×C53
HallC3×C5 ⋊ D17×C53
SylowC5 ⋊ C53×D51
SylowC3 ⋊ C53×D85

Subgroups

subgroupG/H
center, hypercenterC53D255
commutator, cosocle, hypocenterC3×C5×C17C2×C53
FrattiniC1G
Fitting, socleC3×C5×C17×C53C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13515

Conjugacy classes & character table

6837 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27030, 15);