Finite Group Databasebeta

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C3×C5×C7×C79⋊C3 #38733485

order24885
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C7×C79⋊C3
unambiguous semidirect productC79⋊(C32×C5×C7)
unambiguous semidirect product(C3×C79)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C79)⋊(C32×C7)
unambiguous semidirect product(C3×C5×C79)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C79 ⋊ C3
derived, SylowC79 ⋊ C32×C5×C7
HallC5×C7×C79 ⋊ C32
HallC7×C79 ⋊ C32×C5
HallC5×C79 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C79⋊C3
commutator, cosocle, hypocenterC79C32×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C79C3
LCSG ▷ C79
UCSC1 ◁ C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8295

Conjugacy classes & character table

3045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24885, 8);