Finite Group Databasebeta

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C2×D5×C13×#3861 #50304302

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C13×#3861
unambiguous semidirect productC5⋊(C22×C13×#3861)
unambiguous semidirect product(C2×C5)⋊(C2×C13×#3861)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2×C3
derived, HallC5×C72 ⋊ C22×C3×C13
HallC2×C72×D5×C13 ⋊ C3
HallC5×C13×#3861 ⋊ C22
HallC5×C72×C13 ⋊ C22×C3
HallC2×C72×D5 ⋊ C3×C13
HallC5×#3861 ⋊ C22×C13
HallC72×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C22×#3861
SylowC72 ⋊ C2×C3×D5×C13
SylowC5 ⋊ C22×C13×#3861

Subgroups

subgroupG/H
center, hypercenterC2×C13D5×#3861
commutator, cosocle, hypocenterC5×C72C22×C3×C13
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C2×C13

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 988);