Finite Group Databasebeta

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C72×C5⋊AGL(1,𝔽11) #41003990

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

Aliases

direct productC72×C5⋊AGL(1,𝔽11)
unambiguous semidirect productC5⋊(C72×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C72×D5)
unambiguous semidirect productD55⋊(C5×C72)
unambiguous semidirect product(C7×D55)⋊(C5×C7)
unambiguous semidirect product(C72×D55)⋊C5

Splittings

Fitting, socleC5×C72×C11 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C5×C72
HallC5×C72×C11⋊C5 ⋊ C2
HallC72×C11 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C72
SylowC11 ⋊ C5×C72×D5

Subgroups

subgroupG/H
center, hypercenterC72C5⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C2×C5×C72
FrattiniC1G
Fitting, socleC5×C72×C11C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C72

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 57);