Finite Group Databasebeta

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C2×C9×D785 #43246296

order28260
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D785
unambiguous semidirect product(C2×C5)⋊(C9×D157)

Splittings

FittingC2×C5×C9×C157 ⋊ C2
derived, HallC5×C157 ⋊ C22×C9
HallC5×C9×C157 ⋊ C22
HallC9×C157 ⋊ C2×D5
SylowC157 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×D157
SylowC5 ⋊ C2×C9×D157

Subgroups

subgroupG/H
center, hypercenterC2×C9D785
commutator, hypocenterC5×C157C22×C9
FrattiniC3C2×C3×D785
FittingC2×C5×C9×C157C2
socleC2×C3×C5×C157C2×C3
prime radicalC2×C3×D785C3
cosocleC3×C5×C157C22×C3
LCSG ▷ C5×C157
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14130

Conjugacy classes & character table

7092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28260, 50);