Finite Group Databasebeta

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C52×C7×C22⋊(C13⋊C3) #41032079

order27300
automorphism?
homologyAbelianization (H1) = C3×C52×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C7×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C52×C7×C13⋊C3)
unambiguous semidirect productC13⋊(C52×C7×A4)
unambiguous semidirect product(C22×C5)⋊(C5×C7×C13⋊C3)
unambiguous semidirect product(C5×C13)⋊(C5×C7×A4)

Splittings

Fitting, socle, HallC22×C52×C7×C13 ⋊ C3
derived, HallC22×C13 ⋊ C3×C52×C7
HallC52×C7×C13 ⋊ A4
HallC22×C52×C13 ⋊ C3×C7
HallC22×C52×C7 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C3×C52
HallC52×C13 ⋊ C7×A4
HallC22×C52 ⋊ C7×C13⋊C3
HallC7×C13 ⋊ C52×A4
HallC22×C7 ⋊ C52×C13⋊C3
SylowC13 ⋊ C52×C7×A4
SylowC22 ⋊ C52×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC52×C7C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C52×C7
FrattiniC1G
Fitting, socleC22×C52×C7×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C52×C7

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 969);