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C5×D23×AGL(1,𝔽11) #38760756

order25300
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×D23×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C52×D23)
unambiguous semidirect product(D11×D23)⋊C52
unambiguous semidirect product(D23×C11⋊C5)⋊(C2×C5)
unambiguous semidirect product(C23×AGL(1,𝔽11))⋊(C2×C5)
unambiguous semidirect product(C23⋊AGL(1,𝔽11))⋊(C2×C5)
unambiguous semidirect product(C5×D11×D23)⋊C5

Splittings

Fitting, socleC5×C11×C23 ⋊ C22×C5
derived, HallC11×C23 ⋊ C22×C52
HallC5×C23×C11⋊C5 ⋊ C22
HallD11×D23 ⋊ C52
HallC5×C11⋊C5 ⋊ C2×D23
SylowC23 ⋊ C2×C5×AGL(1,𝔽11)
SylowC11 ⋊ C2×C52×D23

Subgroups

subgroupG/H
center, hypercenterC5D23×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C23C22×C52
FrattiniC1G
Fitting, socleC5×C11×C23C22×C5
LCSG ▷ C11×C23
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1265

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 93);