Finite Group Databasebeta

← Prev (#44525543) Next (#44525545) →

C52×C22⋊(C103⋊C3) #44525544

order30900
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C22⋊(C103⋊C3)
unambiguous semidirect productC22⋊(C52×C103⋊C3)
unambiguous semidirect product(C22×C5)⋊(C5×C103⋊C3)
unambiguous semidirect productC103⋊(C52×A4)
unambiguous semidirect product(C5×C103)⋊(C5×A4)

Splittings

Fitting, socle, HallC22×C52×C103 ⋊ C3
derived, HallC22×C103 ⋊ C3×C52
HallC52×C103 ⋊ A4
SylowC103 ⋊ C52×A4
HallC22×C52 ⋊ C103⋊C3
SylowC22 ⋊ C52×C103⋊C3

Subgroups

subgroupG/H
center, hypercenterC52C22⋊(C103⋊C3)
commutator, cosocle, hypocenterC22×C103C3×C52
FrattiniC1G
Fitting, socleC22×C52×C103C3
LCSG ▷ C22×C103
UCSC1 ◁ C52

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10300

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 150);