Finite Group Databasebeta

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C5×D3×C11×C79 #39907626

order26070
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C79 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C11×C79
unambiguous semidirect productC3⋊(C2×C5×C11×C79)

Splittings

Fitting, socle, HallC3×C5×C11×C79 ⋊ C2
derived, SylowC3 ⋊ C2×C5×C11×C79
HallC3×C11×C79 ⋊ C2×C5
HallC3×C5×C79 ⋊ C2×C11
HallC3×C79 ⋊ C2×C5×C11
HallC3×C5×C11 ⋊ C2×C79
HallC3×C11 ⋊ C2×C5×C79
HallC3×C5 ⋊ C2×C11×C79

Subgroups

subgroupG/H
center, hypercenterC5×C11×C79D3
commutator, cosocle, hypocenterC3C2×C5×C11×C79
FrattiniC1G
Fitting, socleC3×C5×C11×C79C2
LCSG ▷ C3
UCSC1 ◁ C5×C11×C79

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13035

Conjugacy classes & character table

13035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26070, 12);