Finite Group Databasebeta

← Prev (#37560984) Next (#37560986) →

C2×D5×#11924776 #37560985

order23940
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×#11924776
unambiguous semidirect productC5⋊(C22×#11924776)
unambiguous semidirect product(C2×C5)⋊(C2×#11924776)

Splittings

derived, HallC5×C7×C19 ⋊ C22×C9
HallC5×#11924776 ⋊ C22
HallC2×C7×D5×C19 ⋊ C9
HallC2×D5×C19 ⋊ C7⋊C9
HallC2×C7×D5 ⋊ #4294
HallC7×C19 ⋊ C2×C9×D5
HallC5×C19 ⋊ C22×C7⋊C9
HallC5×C7 ⋊ C22×#4294
SylowC19 ⋊ C2×D5×C7⋊C9
SylowC7 ⋊ C2×D5×#4294
SylowC5 ⋊ C22×#11924776

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×#87704
commutator, hypocenterC5×C7×C19C22×C9
FrattiniC3C2×D5×#87704
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C7×D5×C19C3
cosocleC3×C5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

1128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 117);