Finite Group Databasebeta

← Prev (#49182137) Next (#49182139) →

C11×C23⋊((C5⋊D5)⋊C3) #49182138

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C23⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C11×C5⋊D115)⋊C3

Splittings

Fitting, socle, HallC52×C11×C23 ⋊ C2×C3
derived, HallC52×C23 ⋊ C2×C3×C11
HallC11×C23×C52⋊C3 ⋊ C2
HallC11×C5⋊D115 ⋊ C3
HallC23×C52⋊C3 ⋊ C2×C11
HallC5⋊D115 ⋊ C3×C11
HallC11×C52⋊C3 ⋊ D23
HallC52×C11 ⋊ C3×D23
HallC11×C23 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C11×D23
SylowC52 ⋊ C3×C11×D23
SylowC23 ⋊ C11×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C23⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C23C2×C3×C11
FrattiniC1G
Fitting, socleC52×C11×C23C2×C3
LCSG ▷ C52×C23
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1441 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 75);