Finite Group Databasebeta

← Prev (#44394680) Next (#44394682) →

C2×C7×C23×C3⋊D15 #44394681

order28980
automorphism?
homologyAbelianization (H1) = C22×C7×C23 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C23×C3⋊D15
unambiguous semidirect product(C2×C3)⋊(C7×C23×D15)
unambiguous semidirect product(C2×C5)⋊(C7×C3⋊D3×C23)

Splittings

Fitting, socleC2×C32×C5×C7×C23 ⋊ C2
derived, HallC32×C5 ⋊ C22×C7×C23
HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C2×D5
HallC32×C5×C23 ⋊ C22×C7
HallC5×C7×C23 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C22×C23
HallC32×C23 ⋊ C2×C7×D5
HallC5×C23 ⋊ C2×C7×C3⋊D3
HallC32×C7 ⋊ C2×D5×C23
HallC5×C7 ⋊ C2×C3⋊D3×C23
SylowC32 ⋊ C2×C7×D5×C23
SylowC5 ⋊ C2×C7×C3⋊D3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C23C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C7×C23
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C23C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C7×C23

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14490

Conjugacy classes & character table

7728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 350);