Finite Group Databasebeta

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C5×#14578979⋊C3 #49179772

order37740
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#14578979⋊C3
unambiguous semidirect product#14578979⋊(C3×C5)
unambiguous semidirect product(C5×#14578979)⋊C3

Splittings

Fitting, socle, HallC5×C17×C37 ⋊ C3×C4
derived, HallC17×C37 ⋊ C3×C4×C5
HallC5×#14578979 ⋊ C3
HallC5×C17×C37⋊C3 ⋊ C4
Hall#14578979 ⋊ C3×C5
HallC17×C37⋊C3 ⋊ C4×C5
HallC5×C37⋊C3 ⋊ #595
HallC5×C37 ⋊ C3×#595
HallC37⋊C3 ⋊ C5×#595
HallC5×C17 ⋊ #3866⋊C3
SylowC37 ⋊ C3×C5×#595
SylowC17 ⋊ C5×#3866⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#14578979⋊C3
commutator, hypocenterC17×C37C3×C4×C5
FrattiniC1G
Fitting, socleC5×C17×C37C3×C4
prime radicalC5×C17⋊(D37⋊C3)C2
cosocleD629C2×C3×C5
LCSG ▷ C17×C37
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 27);