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C2×C5⋊(C23⋊AGL(1,𝔽11)) #38760772

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

Aliases

direct productC2×C5⋊(C23⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C5)⋊(C23⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C23)⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D115
unambiguous semidirect product(C2×D1265)⋊C5

Splittings

Fitting, socleC2×C5×C11×C23 ⋊ C2×C5
derivedC5×C11×C23 ⋊ C22×C5
HallC5×C23×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D23
HallC11×C23 ⋊ C2×C5×D5
SylowC23 ⋊ C2×C5⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D115

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C23⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC5×C11×C23C22×C5
FrattiniC1G
Fitting, socleC2×C5×C11×C23C2×C5
LCSG ▷ C5×C11×C23
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2530

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 109);