Finite Group Databasebeta

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C2×C5×C13⋊C3×C73 #43249684

order28470
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C73 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13⋊C3×C73
unambiguous semidirect product(C2×C13)⋊(C3×C5×C73)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C73)

Splittings

Fitting, socle, HallC2×C5×C13×C73 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C73
HallC5×C13×C73 ⋊ C2×C3
HallC2×C13×C73 ⋊ C3×C5
HallC13×C73 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C73
HallC5×C13 ⋊ C2×C3×C73
HallC2×C13 ⋊ C3×C5×C73

Subgroups

subgroupG/H
center, hypercenterC2×C5×C73C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C73
FrattiniC1G
Fitting, socleC2×C5×C13×C73C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C73

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9490

Conjugacy classes & character table

5110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28470, 3);