Finite Group Databasebeta

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C53×D285 #44475014

order30210
automorphism?
homologyAbelianization (H1) = C2×C53 · Schur multiplier (H2) = C1

Aliases

direct productC53×D285
unambiguous semidirect productC3⋊(C53×D95)
unambiguous semidirect productC5⋊(C53×D57)
unambiguous semidirect productC19⋊(D15×C53)

Splittings

Fitting, socle, HallC3×C5×C19×C53 ⋊ C2
derived, HallC3×C5×C19 ⋊ C2×C53
HallC5×C19×C53 ⋊ D3
HallC3×C19×C53 ⋊ D5
HallC19×C53 ⋊ D15
HallC3×C5×C53 ⋊ D19
HallC5×C53 ⋊ D57
HallC3×C53 ⋊ D95
HallC5×C19 ⋊ D3×C53
HallC3×C19 ⋊ D5×C53
SylowC19 ⋊ D15×C53
HallC3×C5 ⋊ D19×C53
SylowC5 ⋊ C53×D57
SylowC3 ⋊ C53×D95

Subgroups

subgroupG/H
center, hypercenterC53D285
commutator, cosocle, hypocenterC3×C5×C19C2×C53
FrattiniC1G
Fitting, socleC3×C5×C19×C53C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15105

Conjugacy classes & character table

7632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30210, 16);