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C2×C25×AGL(1,𝔽23) #38760684

order25300
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C2×C11×C25)
unambiguous semidirect product(C2×D23)⋊(C11×C25)
unambiguous semidirect product(C23⋊C11)⋊(C22×C25)
unambiguous semidirect product(C2×C23⋊C11)⋊(C2×C25)
unambiguous semidirect product(C2×C25×D23)⋊C11

Splittings

FittingC2×C23×C25 ⋊ C2×C11
derived, SylowC23 ⋊ C22×C11×C25
HallC25×C23⋊C11 ⋊ C22
HallC2×C25×D23 ⋊ C11
HallC23×C25 ⋊ C22×C11
HallC23⋊C11 ⋊ C22×C25
HallC2×D23 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25AGL(1,𝔽23)
commutator, hypocenterC23C22×C11×C25
FrattiniC5C2×C5×AGL(1,𝔽23)
FittingC2×C23×C25C2×C11
socleC2×C5×C23C2×C5×C11
prime radicalC2×C5×AGL(1,𝔽23)C5
cosocleC5×C23C22×C5×C11
LCSG ▷ C23
UCSC1 ◁ C2×C25

60 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, 21);