Finite Group Databasebeta

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C37×D345 #38784288

order25530
automorphism?
homologyAbelianization (H1) = C2×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×D345
unambiguous semidirect productC3⋊(C37×D115)
unambiguous semidirect productC5⋊(C37×D69)
unambiguous semidirect productC23⋊(D15×C37)

Splittings

Fitting, socle, HallC3×C5×C23×C37 ⋊ C2
derived, HallC3×C5×C23 ⋊ C2×C37
HallC5×C23×C37 ⋊ D3
HallC3×C23×C37 ⋊ D5
HallC23×C37 ⋊ D15
HallC3×C5×C37 ⋊ D23
HallC5×C37 ⋊ D69
HallC5×C23 ⋊ D3×C37
HallC3×C37 ⋊ D115
HallC3×C23 ⋊ D5×C37
SylowC23 ⋊ D15×C37
HallC3×C5 ⋊ C37×D23
SylowC5 ⋊ C37×D69
SylowC3 ⋊ C37×D115

Subgroups

subgroupG/H
center, hypercenterC37D345
commutator, cosocle, hypocenterC3×C5×C23C2×C37
FrattiniC1G
Fitting, socleC3×C5×C23×C37C2
LCSG ▷ C3×C5×C23
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12765

Conjugacy classes & character table

6438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25530, 16);