Finite Group Databasebeta

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C5×D13⋊C3×C97 #49180809

order37830
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productC5×D13⋊C3×C97
unambiguous semidirect productD13⋊(C3×C5×C97)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C97)
unambiguous semidirect product(C5×D13)⋊(C3×C97)

Splittings

Fitting, socle, HallC5×C13×C97 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C97
HallC5×C13⋊C3×C97 ⋊ C2
HallC5×D13×C97 ⋊ C3
HallC13⋊C3×C97 ⋊ C2×C5
HallD13×C97 ⋊ C3×C5
HallC13×C97 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C97
HallC5×D13 ⋊ C3×C97
HallC5×C13 ⋊ C2×C3×C97
HallC13⋊C3 ⋊ C2×C5×C97
HallD13 ⋊ C3×C5×C97

Subgroups

subgroupG/H
center, hypercenterC5×C97D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C97
FrattiniC1G
Fitting, socleC5×C13×C97C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C97

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6305

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37830, 26);