Finite Group Databasebeta

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C13×C3⋊D285 #36372737

order22230
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×C3⋊D285
unambiguous semidirect productC3⋊(C13×D285)
unambiguous semidirect productC5⋊(C13×C3⋊D57)
unambiguous semidirect productC19⋊(C13×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C13×C19 ⋊ C2
derived, HallC32×C5×C19 ⋊ C2×C13
HallC32×C13×C19 ⋊ D5
HallC5×C13×C19 ⋊ C3⋊D3
HallC32×C5×C13 ⋊ D19
HallC13×C19 ⋊ C3⋊D15
HallC32×C19 ⋊ D5×C13
HallC32×C13 ⋊ D95
HallC5×C19 ⋊ C13×C3⋊D3
HallC5×C13 ⋊ C3⋊D57
HallC32×C5 ⋊ C13×D19
SylowC19 ⋊ C13×C3⋊D15
SylowC32 ⋊ C13×D95
SylowC5 ⋊ C13×C3⋊D57

Subgroups

subgroupG/H
center, hypercenterC13C3⋊D285
commutator, cosocle, hypocenterC32×C5×C19C2×C13
FrattiniC1G
Fitting, socleC32×C5×C13×C19C2
LCSG ▷ C32×C5×C19
UCSC1 ◁ C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11115

Conjugacy classes & character table

5577 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22230, 166);