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C2×C52×AGL(1,𝔽23) #38760751

order25300
automorphism?
homologyAbelianization (H1) = C22×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C2×C52×C11)
unambiguous semidirect product(C2×D23)⋊(C52×C11)
unambiguous semidirect product(C23⋊C11)⋊(C22×C52)
unambiguous semidirect product(C2×C5×D23)⋊(C5×C11)
unambiguous semidirect product(C2×C23⋊C11)⋊(C2×C52)
unambiguous semidirect product(C2×C52×D23)⋊C11

Splittings

Fitting, socleC2×C52×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C22×C52×C11
HallC52×C23⋊C11 ⋊ C22
HallC2×C52×D23 ⋊ C11
HallC52×C23 ⋊ C22×C11
HallC23⋊C11 ⋊ C22×C52
HallC2×D23 ⋊ C52×C11

Subgroups

subgroupG/H
center, hypercenterC2×C52AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C22×C52×C11
FrattiniC1G
Fitting, socleC2×C52×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C2×C52

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1150

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 88);