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C5×C22⋊(C373⋊C3) #36375495

order22380
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊(C373⋊C3)
unambiguous semidirect productC22⋊(C5×C373⋊C3)
unambiguous semidirect product(C22×C5)⋊(C373⋊C3)
unambiguous semidirect productC373⋊(C5×A4)
unambiguous semidirect product(C5×C373)⋊A4

Splittings

Fitting, socle, HallC22×C5×C373 ⋊ C3
derived, HallC22×C373 ⋊ C3×C5
HallC5×C373 ⋊ A4
SylowC373 ⋊ C5×A4
HallC22×C5 ⋊ C373⋊C3
SylowC22 ⋊ C5×C373⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C22⋊(C373⋊C3)
commutator, cosocle, hypocenterC22×C373C3×C5
FrattiniC1G
Fitting, socleC22×C5×C373C3
LCSG ▷ C22×C373
UCSC1 ◁ C5

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7460

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22380, 44);