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D11×C25×AGL(1,𝔽7) #37528241

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productD11×C25×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×D11×C25)
unambiguous semidirect product(D7×D11×C25)⋊C3

Splittings

Fitting, HallC7×C11×C25 ⋊ C22×C3
derived, HallC7×C11 ⋊ C22×C3×C25
HallD7×D11×C25 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C22
HallΓL(1,𝔽8)×C25 ⋊ C2×D11
HallD7×D11 ⋊ C3×C25
HallC11×C25 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C22×C25
HallC7×C25 ⋊ C2×C3×D11
HallΓL(1,𝔽8) ⋊ C2×D11×C25
SylowC11 ⋊ C2×C25×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D11×C25

Subgroups

subgroupG/H
center, hypercenterC25D11×AGL(1,𝔽7)
commutator, hypocenterC7×C11C22×C3×C25
FrattiniC5C5×D11×AGL(1,𝔽7)
FittingC7×C11×C25C22×C3
socle, cosocleC5×C7×C11C22×C3×C5
prime radicalC5×D11×AGL(1,𝔽7)C5
LCSG ▷ C7×C11
UCSC1 ◁ C25

120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1925

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 52);