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D11×ΓL(1,𝔽8)⋊D25 #37528246

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

Aliases

direct productD11×ΓL(1,𝔽8)⋊D25
unambiguous semidirect product(ΓL(1,𝔽8)×D11)⋊D25
unambiguous semidirect product(D11×C25)⋊AGL(1,𝔽7)
unambiguous semidirect product(D11×D175)⋊C3

Splittings

Fitting, derived, HallC7×C11×C25 ⋊ C22×C3
HallD11×D175 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C22
HallΓL(1,𝔽8)×C25 ⋊ C2×D11
HallC11×C25 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C2×D25
HallC7×C25 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D25
SylowC25 ⋊ D11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D11×D25
SylowC11 ⋊ C2×ΓL(1,𝔽8)⋊D25
SylowC7 ⋊ C3×D11×D25

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C11×C25C22×C3
FrattiniC5D11×C5⋊AGL(1,𝔽7)
socleC5×C7×C11C2×C3×D5
LCSG ▷ C7×C11×C25
UCSC1

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 57);