Finite Group Databasebeta

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C2×C5×C13⋊C3×C61 #37558159

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C61 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13⋊C3×C61
unambiguous semidirect product(C2×C13)⋊(C3×C5×C61)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C61)

Splittings

Fitting, socle, HallC2×C5×C13×C61 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C61
HallC5×C13×C61 ⋊ C2×C3
HallC2×C13×C61 ⋊ C3×C5
HallC13×C61 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C61
HallC5×C13 ⋊ C2×C3×C61
HallC2×C13 ⋊ C3×C5×C61

Subgroups

subgroupG/H
center, hypercenterC2×C5×C61C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C61
FrattiniC1G
Fitting, socleC2×C5×C13×C61C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C61

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7930

Conjugacy classes & character table

4270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 4);