Finite Group Databasebeta

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C49⋊C3×D115 #46798918

order33810
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC49⋊C3×D115
unambiguous semidirect productC5⋊(D23×C49⋊C3)
unambiguous semidirect productC23⋊(D5×C49⋊C3)
unambiguous semidirect product(C49×D115)⋊C3

Splittings

Fitting, derived, HallC5×C23×C49 ⋊ C2×C3
HallC5×C23×C49⋊C3 ⋊ C2
HallC49×D115 ⋊ C3
HallC23×C49⋊C3 ⋊ D5
HallC23×C49 ⋊ C3×D5
HallC5×C49⋊C3 ⋊ D23
HallC5×C49 ⋊ C3×D23
HallC5×C23 ⋊ C2×C49⋊C3
SylowC49 ⋊ C3×D115
SylowC23 ⋊ D5×C49⋊C3
SylowC5 ⋊ D23×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C23×C49C2×C3
FrattiniC7ΓL(1,𝔽8)×D115
socleC5×C7×C23C2×ΓL(1,𝔽8)
LCSG ▷ C5×C23×C49
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5635

Conjugacy classes & character table

1121 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 22);