Finite Group Databasebeta

← Prev (#37562784) Next (#37562786) →

C3×C5×C11×D73 #37562785

order24090
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D73

Splittings

Fitting, socle, HallC3×C5×C11×C73 ⋊ C2
derived, SylowC73 ⋊ C2×C3×C5×C11
HallC5×C11×C73 ⋊ C2×C3
HallC3×C11×C73 ⋊ C2×C5
HallC3×C5×C73 ⋊ C2×C11
HallC11×C73 ⋊ C2×C3×C5
HallC5×C73 ⋊ C2×C3×C11
HallC3×C73 ⋊ C2×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D73
commutator, cosocle, hypocenterC73C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C73C2
LCSG ▷ C73
UCSC1 ◁ C3×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12045

Conjugacy classes & character table

6270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24090, 5);