Finite Group Databasebeta

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C5×C72×AGL(1,𝔽11) #41003985

order26950
automorphism?
homologyAbelianization (H1) = C2×C52×C72 · Schur multiplier (H2) = C5×C7

Aliases

direct productC5×C72×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C52×C72)
unambiguous semidirect product(C11⋊C5)⋊(C2×C5×C72)
unambiguous semidirect product(C5×D11)⋊(C5×C72)
unambiguous semidirect product(C7×D11)⋊(C52×C7)
unambiguous semidirect product(C5×C7×D11)⋊(C5×C7)
unambiguous semidirect product(C72×D11)⋊C52
unambiguous semidirect product(C5×C72×D11)⋊C5

Splittings

Fitting, socleC5×C72×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C52×C72
HallC5×C72×C11⋊C5 ⋊ C2
HallC72×D11 ⋊ C52
HallC72×C11 ⋊ C2×C52
HallC5×C11⋊C5 ⋊ C2×C72
HallD11 ⋊ C52×C72

Subgroups

subgroupG/H
center, hypercenterC5×C72AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C52×C72
FrattiniC1G
Fitting, socleC5×C72×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C5×C72

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

2695 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 52);