Finite Group Databasebeta

← Prev (#37557198) Next (#37557200) →

C5×D5×D79⋊C3 #37557199

order23700
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D5×D79⋊C3
unambiguous semidirect productD79⋊(C3×C5×D5)
unambiguous semidirect product(D5×D79)⋊(C3×C5)
unambiguous semidirect product(C5×D79⋊C3)⋊(C2×C5)
unambiguous semidirect product(D5×C79⋊C3)⋊(C2×C5)
unambiguous semidirect product(C5⋊(D79⋊C3))⋊(C2×C5)
unambiguous semidirect product(C5×D5×D79)⋊C3

Splittings

Fitting, socle, HallC52×C79 ⋊ C22×C3
derivedC5×C79 ⋊ C22×C3×C5
HallC5×D5×D79 ⋊ C3
HallC52×C79⋊C3 ⋊ C22
HallC79⋊C3 ⋊ C2×C5×D5
SylowC79 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C2×D79⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D5×D79⋊C3
commutator, cosocle, hypocenterC5×C79C22×C3×C5
FrattiniC1G
Fitting, socleC52×C79C22×C3
LCSG ▷ C5×C79
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 790

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 82);