Finite Group Databasebeta

← Prev (#44394682) Next (#44394684) →

C2×C23×C3⋊D105 #44394683

order28980
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C23×C3⋊D105
unambiguous semidirect product(C2×C3)⋊(C23×D105)
unambiguous semidirect product(C2×C5)⋊(C23×C3⋊D21)
unambiguous semidirect product(C2×C7)⋊(C23×C3⋊D15)

Splittings

Fitting, socleC2×C32×C5×C7×C23 ⋊ C2
derived, HallC32×C5×C7 ⋊ C22×C23
HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C2×D5
HallC32×C5×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×C3⋊D3
HallC32×C23 ⋊ C2×D35
HallC7×C23 ⋊ C2×C3⋊D15
HallC5×C23 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×D5×C23
HallC32×C5 ⋊ C2×D7×C23
HallC5×C7 ⋊ C2×C3⋊D3×C23
SylowC32 ⋊ C2×C23×D35
SylowC7 ⋊ C2×C23×C3⋊D15
SylowC5 ⋊ C2×C23×C3⋊D21

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C22×C23
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C23C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C2×C23

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14490

Conjugacy classes & character table

7314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 352);