Finite Group Databasebeta

← Prev (#37567557) Next (#37567559) →

C2×C3×C11⋊C5×D37 #37567558

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11⋊C5×D37
unambiguous semidirect product(C2×C3×C11×D37)⋊C5

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C5
derived, HallC11×C37 ⋊ C22×C3×C5
HallC3×C37×C11⋊C5 ⋊ C22
HallC2×C3×C11×D37 ⋊ C5
HallC37×C11⋊C5 ⋊ C22×C3
HallC2×C11×D37 ⋊ C3×C5
HallC3×C11×C37 ⋊ C22×C5
HallC3×C37 ⋊ C22×C11⋊C5
SylowC37 ⋊ C22×C3×C11⋊C5
HallC3×C11 ⋊ C2×C5×D37
SylowC11 ⋊ C2×C3×C5×D37

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×D37
commutator, cosocle, hypocenterC11×C37C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C5
LCSG ▷ C11×C37
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 79);