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C49⋊C3×D85 #38735932

order24990
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC49⋊C3×D85
unambiguous semidirect productC5⋊(D17×C49⋊C3)
unambiguous semidirect productC17⋊(D5×C49⋊C3)
unambiguous semidirect product(C49×D85)⋊C3

Splittings

Fitting, derived, HallC5×C17×C49 ⋊ C2×C3
HallC5×C17×C49⋊C3 ⋊ C2
HallC49×D85 ⋊ C3
HallC17×C49⋊C3 ⋊ D5
HallC17×C49 ⋊ C3×D5
HallC5×C49⋊C3 ⋊ D17
HallC5×C49 ⋊ C3×D17
HallC5×C17 ⋊ C2×C49⋊C3
SylowC49 ⋊ C3×D85
SylowC17 ⋊ D5×C49⋊C3
SylowC5 ⋊ D17×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C17×C49C2×C3
FrattiniC7ΓL(1,𝔽8)×D85
socleC5×C7×C17C2×ΓL(1,𝔽8)
LCSG ▷ C5×C17×C49
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4165

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 22);