Finite Group Databasebeta

← Prev (#37528229) Next (#37528231) →

C2×ΓL(1,𝔽8)×D11⋊C25 #37528230

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

Aliases

direct productC2×ΓL(1,𝔽8)×D11⋊C25
unambiguous semidirect productD11⋊(C2×ΓL(1,𝔽8)×C25)
unambiguous semidirect product(C2×D11)⋊(ΓL(1,𝔽8)×C25)
unambiguous semidirect product(C11⋊C25)⋊(C22×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C11⋊C25)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(C2×ΓL(1,𝔽8)×D11)⋊C25
unambiguous semidirect product(C2×C7×D11⋊C25)⋊C3

Splittings

derived, HallC7×C11 ⋊ C22×C3×C25
HallC2×C7×D11⋊C25 ⋊ C3
HallΓL(1,𝔽8)×C11⋊C25 ⋊ C22
HallC7×C11⋊C25 ⋊ C22×C3
HallC2×ΓL(1,𝔽8)×D11 ⋊ C25
HallC2×C7×D11 ⋊ C3×C25
HallC11⋊C25 ⋊ C22×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C22×C25
HallC2×D11 ⋊ ΓL(1,𝔽8)×C25
SylowC11 ⋊ C22×ΓL(1,𝔽8)×C25
SylowC7 ⋊ C2×C3×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×AGL(1,𝔽11)
commutator, hypocenterC7×C11C22×C3×C25
FrattiniC5C2×ΓL(1,𝔽8)×AGL(1,𝔽11)
Fitting, socleC2×C5×C7×C11C2×C3×C5
prime radicalC2×C5×ΓL(1,𝔽8)×D11C5
cosocleC5×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 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) = 3850

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 41);