Finite Group Databasebeta

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C2×C3×C11⋊C5×C79 #39907616

order26070
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C79 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C11⋊C5×C79
unambiguous semidirect product(C2×C11)⋊(C3×C5×C79)
unambiguous semidirect product(C2×C3×C11)⋊(C5×C79)
unambiguous semidirect product(C2×C3×C11×C79)⋊C5

Splittings

Fitting, socle, HallC2×C3×C11×C79 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C79
HallC3×C11×C79 ⋊ C2×C5
HallC2×C11×C79 ⋊ C3×C5
HallC11×C79 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C79
HallC3×C11 ⋊ C2×C5×C79
HallC2×C11 ⋊ C3×C5×C79

Subgroups

subgroupG/H
center, hypercenterC2×C3×C79C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C79
FrattiniC1G
Fitting, socleC2×C3×C11×C79C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C79

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5214

Conjugacy classes & character table

3318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26070, 2);