Finite Group Databasebeta

← Prev (#37528231) Next (#37528233) →

D3×C7×D11⋊C25 #37528232

order23100
automorphism?
homologyAbelianization (H1) = C22×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D11⋊C25
unambiguous semidirect productD11⋊(D3×C7×C25)
unambiguous semidirect product(D3×D11)⋊(C7×C25)
unambiguous semidirect product(D3×C7×D11)⋊C25
unambiguous semidirect product(C3×D11⋊C25)⋊(C2×C7)
unambiguous semidirect product(D3×C11⋊C25)⋊(C2×C7)
unambiguous semidirect product(C3⋊(D11⋊C25))⋊(C2×C7)

Splittings

derived, HallC3×C11 ⋊ C22×C7×C25
HallC3×C7×C11⋊C25 ⋊ C22
HallC7×C11⋊C25 ⋊ C2×D3
HallD3×C7×D11 ⋊ C25
HallC3×C11⋊C25 ⋊ C22×C7
HallC11⋊C25 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C22×C25
HallD3×D11 ⋊ C7×C25
HallC7×C11 ⋊ C2×D3×C25
HallC3×C7 ⋊ C2×D11⋊C25
SylowC11 ⋊ C2×D3×C7×C25
SylowC3 ⋊ C2×C7×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC5×C7D3×AGL(1,𝔽11)
commutator, hypocenterC3×C11C22×C7×C25
FrattiniC5D3×C7×AGL(1,𝔽11)
Fitting, socleC3×C5×C7×C11C22×C5
prime radicalC5×D3×C7×D11C5
cosocleC3×C5×C11C22×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C5×C7

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 5775

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 43);