Finite Group Databasebeta

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C5×D5×C13×C49 #44541600

order31850
automorphism?
homologyAbelianization (H1) = C2×C5×C13×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×D5×C13×C49
unambiguous semidirect productC5⋊(C2×C5×C13×C49)

Splittings

Fitting, HallC52×C13×C49 ⋊ C2
derivedC5 ⋊ C2×C5×C13×C49
HallC52×C49 ⋊ C2×C13
HallC52×C13 ⋊ C2×C49
SylowC52 ⋊ C2×C13×C49

Subgroups

subgroupG/H
center, hypercenterC5×C13×C49D5
commutator, hypocenterC5C2×C5×C13×C49
FrattiniC7C5×C7×D5×C13
FittingC52×C13×C49C2
socleC52×C7×C13C2×C7
prime radicalC5×C7×D5×C13C7
cosocleC5×C7C2×C5×C7×C13
LCSG ▷ C5
UCSC1 ◁ C5×C13×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

12740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31850, 13);