Finite Group Databasebeta

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C5×A4×C17×C23 #37553350

order23460
automorphism?
homologyAbelianization (H1) = C3×C5×C17×C23 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C17×C23
unambiguous semidirect productC22⋊(C3×C5×C17×C23)
unambiguous semidirect product(C22×C5)⋊(C3×C17×C23)
unambiguous semidirect product(C22×C17)⋊(C3×C5×C23)
unambiguous semidirect product(C22×C23)⋊(C3×C5×C17)
unambiguous semidirect product(C22×C5×C17)⋊(C3×C23)
unambiguous semidirect product(C22×C5×C23)⋊(C3×C17)
unambiguous semidirect product(C22×C17×C23)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C17×C23)⋊C3

Splittings

Fitting, socle, HallC22×C5×C17×C23 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C17×C23
HallC22×C17×C23 ⋊ C3×C5
HallC22×C5×C23 ⋊ C3×C17
HallC22×C5×C17 ⋊ C3×C23
HallC22×C23 ⋊ C3×C5×C17
HallC22×C17 ⋊ C3×C5×C23
HallC22×C5 ⋊ C3×C17×C23

Subgroups

subgroupG/H
center, hypercenterC5×C17×C23A4
commutator, cosocle, hypocenterC22C3×C5×C17×C23
FrattiniC1G
Fitting, socleC22×C5×C17×C23C3
LCSG ▷ C22
UCSC1 ◁ C5×C17×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7820

Conjugacy classes & character table

7820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 77);