Finite Group Databasebeta

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C79×D231 #49140959

order36498
automorphism?
homologyAbelianization (H1) = C2×C79 · Schur multiplier (H2) = C1

Aliases

direct productC79×D231
unambiguous semidirect productC3⋊(C79×D77)
unambiguous semidirect productC7⋊(D33×C79)
unambiguous semidirect productC11⋊(D21×C79)

Splittings

Fitting, socle, HallC3×C7×C11×C79 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C79
HallC7×C11×C79 ⋊ D3
HallC3×C11×C79 ⋊ D7
HallC3×C7×C79 ⋊ D11
HallC11×C79 ⋊ D21
HallC7×C79 ⋊ D33
HallC3×C79 ⋊ D77
HallC7×C11 ⋊ D3×C79
HallC3×C11 ⋊ D7×C79
HallC3×C7 ⋊ D11×C79
SylowC11 ⋊ D21×C79
SylowC7 ⋊ D33×C79
SylowC3 ⋊ C79×D77

Subgroups

subgroupG/H
center, hypercenterC79D231
commutator, cosocle, hypocenterC3×C7×C11C2×C79
FrattiniC1G
Fitting, socleC3×C7×C11×C79C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C79

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18249

Conjugacy classes & character table

9243 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36498, 19);