Finite Group Databasebeta

← Prev (#46831407) Next (#46831409) →

C3×C3⋊(C7⋊(D11⋊C25)) #46831408

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(C7⋊(D11⋊C25))
unambiguous semidirect productC3⋊(C3×C7⋊(D11⋊C25))
unambiguous semidirect product(C11⋊C25)⋊(C3×D21)
unambiguous semidirect product(C3×D231)⋊C25

Splittings

derivedC3×C7×C11 ⋊ C2×C3×C25
HallC32×C7×C11⋊C25 ⋊ C2
HallC32×C11⋊C25 ⋊ D7
HallC7×C11⋊C25 ⋊ C3×D3
HallC3×D231 ⋊ C25
HallC32×C7×C11 ⋊ C2×C25
HallC11⋊C25 ⋊ C3×D21
HallC32×C11 ⋊ D7×C25
HallC7×C11 ⋊ C3×D3×C25
HallC32×C7 ⋊ D11⋊C25
SylowC11 ⋊ C3×C25×D21
SylowC32 ⋊ C7⋊(D11⋊C25)
SylowC7 ⋊ C3×C3⋊(D11⋊C25)

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊(C7⋊AGL(1,𝔽11))
commutator, hypocenterC3×C7×C11C2×C3×C25
FrattiniC5C3×C3⋊(C7⋊AGL(1,𝔽11))
Fitting, socleC32×C5×C7×C11C2×C5
prime radicalC3×C5×D231C5
cosocleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3×C5

108 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 11550

Conjugacy classes & character table

1215 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 51);