Finite Group Databasebeta

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C5×D2379 #37558176

order23790
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2379
unambiguous semidirect productC3⋊(C5×D793)
unambiguous semidirect productC13⋊(C5×D183)

Splittings

Fitting, socle, HallC3×C5×C13×C61 ⋊ C2
derived, HallC3×C13×C61 ⋊ C2×C5
HallC5×C13×C61 ⋊ D3
HallC3×C5×C61 ⋊ D13
HallC13×C61 ⋊ C5×D3
HallC5×C61 ⋊ D39
HallC3×C5×C13 ⋊ D61
HallC3×C61 ⋊ C5×D13
HallC5×C13 ⋊ D183
SylowC61 ⋊ C5×D39
HallC3×C13 ⋊ C5×D61
HallC3×C5 ⋊ D793
SylowC13 ⋊ C5×D183
SylowC3 ⋊ C5×D793

Subgroups

subgroupG/H
center, hypercenterC5D2379
commutator, cosocle, hypocenterC3×C13×C61C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C61C2
LCSG ▷ C3×C13×C61
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11895

Conjugacy classes & character table

5955 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 21);