Finite Group Databasebeta

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C2×C3×C5×C53⋊C13 #35207759

order20670
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C5×C53⋊C13
unambiguous semidirect product(C2×C53)⋊(C3×C5×C13)
unambiguous semidirect product(C2×C3×C53)⋊(C5×C13)
unambiguous semidirect product(C2×C5×C53)⋊(C3×C13)
unambiguous semidirect product(C2×C3×C5×C53)⋊C13

Splittings

Fitting, socle, HallC2×C3×C5×C53 ⋊ C13
derived, SylowC53 ⋊ C2×C3×C5×C13
HallC3×C5×C53 ⋊ C2×C13
HallC2×C5×C53 ⋊ C3×C13
HallC2×C3×C53 ⋊ C5×C13
HallC5×C53 ⋊ C2×C3×C13
HallC3×C53 ⋊ C2×C5×C13
HallC2×C53 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C53⋊C13
commutator, cosocle, hypocenterC53C2×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C53C13
LCSG ▷ C53
UCSC1 ◁ C2×C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1590

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20670, 2);