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C17×#10625191⋊C3 #49179778

order37740
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×#10625191⋊C3
unambiguous semidirect product#10625191⋊(C3×C17)
unambiguous semidirect product(C17×#10625191)⋊C3

Splittings

Fitting, socle, HallC5×C17×C37 ⋊ C3×C4
derived, HallC5×C37 ⋊ C3×C4×C17
HallC17×#10625191 ⋊ C3
HallC5×C17×C37⋊C3 ⋊ C4
HallC17×C37⋊C3 ⋊ AGL(1,𝔽5)
Hall#10625191 ⋊ C3×C17
HallC17×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C37⋊C3 ⋊ C4×C17
HallC37⋊C3 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ #3866⋊C3
SylowC37 ⋊ C3×C17×AGL(1,𝔽5)
SylowC5 ⋊ C17×#3866⋊C3

Subgroups

subgroupG/H
center, hypercenterC17#10625191⋊C3
commutator, hypocenterC5×C37C3×C4×C17
FrattiniC1G
Fitting, socleC5×C17×C37C3×C4
prime radicalC17×C5⋊(D37⋊C3)C2
cosocleD185C2×C3×C17
LCSG ▷ C5×C37
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 33);