Finite Group Databasebeta

← Prev (#39910742) Next (#39910744) →

D19⋊C3×D115 #39910743

order26220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD19⋊C3×D115
unambiguous semidirect productD19⋊(C3×D115)
unambiguous semidirect product(C5×D19⋊C3)⋊D23
unambiguous semidirect product(C23×D19⋊C3)⋊D5
unambiguous semidirect product(D19×D115)⋊C3

Splittings

Fitting, socle, derived, HallC5×C19×C23 ⋊ C22×C3
HallD19×D115 ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C22
HallC23×C19⋊C3 ⋊ C2×D5
HallC19×C23 ⋊ C2×C3×D5
HallC5×C19⋊C3 ⋊ C2×D23
HallC5×C23 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D23
HallC19⋊C3 ⋊ C2×D115
SylowC23 ⋊ D5×D19⋊C3
SylowC19 ⋊ C2×C3×D115
SylowC5 ⋊ D23×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C23C22×C3
LCSG ▷ C5×C19×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2185

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 33);