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D5×C23×AGL(1,𝔽11) #38760762

order25300
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productD5×C23×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×D5×C23)
unambiguous semidirect product(D5×D11)⋊(C5×C23)
unambiguous semidirect product(C5×AGL(1,𝔽11))⋊(C2×C23)
unambiguous semidirect product(D5×C11⋊C5)⋊(C2×C23)
unambiguous semidirect product(C5⋊AGL(1,𝔽11))⋊(C2×C23)
unambiguous semidirect product(D5×D11×C23)⋊C5

Splittings

Fitting, socleC5×C11×C23 ⋊ C22×C5
derivedC5×C11 ⋊ C22×C5×C23
HallC5×C23×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C23
HallC11×C23 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C5×D5×C23

Subgroups

subgroupG/H
center, hypercenterC23D5×AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C22×C5×C23
FrattiniC1G
Fitting, socleC5×C11×C23C22×C5
LCSG ▷ C5×C11
UCSC1 ◁ C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1265

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 99);