Finite Group Databasebeta

← Prev (#46800913) Next (#46800915) →

C2×C5×C11×C103⋊C3 #46800914

order33990
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×C103⋊C3
unambiguous semidirect product(C2×C103)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C5×C103)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C103)⋊C3

Splittings

Fitting, socle, HallC2×C5×C11×C103 ⋊ C3
derived, SylowC103 ⋊ C2×C3×C5×C11
HallC5×C11×C103 ⋊ C2×C3
HallC2×C11×C103 ⋊ C3×C5
HallC11×C103 ⋊ C2×C3×C5
HallC2×C5×C103 ⋊ C3×C11
HallC5×C103 ⋊ C2×C3×C11
HallC2×C103 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C103⋊C3
commutator, cosocle, hypocenterC103C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C103C3
LCSG ▷ C103
UCSC1 ◁ C2×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11330

Conjugacy classes & character table

4070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 3);