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C2×C5×D423 #22554875

order8460
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D423
unambiguous semidirect product(C2×C9)⋊(C5×D47)
unambiguous semidirect product(C2×C47)⋊(C5×D9)

Splittings

FittingC2×C5×C9×C47 ⋊ C2
derived, HallC9×C47 ⋊ C22×C5
HallC5×C9×C47 ⋊ C22
HallC5×C47 ⋊ C2×D9
SylowC47 ⋊ C2×C5×D9
HallC5×C9 ⋊ C2×D47
SylowC9 ⋊ C2×C5×D47

Subgroups

subgroupG/H
center, hypercenterC2×C5D423
commutator, hypocenterC9×C47C22×C5
FrattiniC3C2×C5×D141
FittingC2×C5×C9×C47C2
socleC2×C3×C5×C47D3
LCSG ▷ C9×C47
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8460, 24);