Finite Group Databasebeta

← Prev (#44526250) Next (#44526252) →

C3⋊(C7⋊(D67⋊C11)) #44526251

order30954
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C7⋊(D67⋊C11))
unambiguous semidirect productC7⋊(C3⋊(D67⋊C11))
unambiguous semidirect product(C67⋊C11)⋊D21
unambiguous semidirect productD1407⋊C11

Splittings

Fitting, socle, derived, HallC3×C7×C67 ⋊ C2×C11
HallC3×C7×C67⋊C11 ⋊ C2
HallC7×C67⋊C11 ⋊ D3
HallD1407 ⋊ C11
HallC3×C67⋊C11 ⋊ D7
HallC67⋊C11 ⋊ D21
HallC7×C67 ⋊ D3×C11
HallC3×C67 ⋊ C11×D7
SylowC67 ⋊ C11×D21
HallC3×C7 ⋊ D67⋊C11
SylowC7 ⋊ C3⋊(D67⋊C11)
SylowC3 ⋊ C7⋊(D67⋊C11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C67C2×C11
LCSG ▷ C3×C7×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1407

Polycyclic presentation:

2,3,7,11,67|b^a=b^2,c^a=c^6,e^a=e^66,e^d=e^64

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 32);