Finite Group Databasebeta

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C3×C5×C491⋊C5 #49145684

order36825
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C491⋊C5
unambiguous semidirect productC491⋊(C3×C52)
unambiguous semidirect product(C3×C491)⋊C52
unambiguous semidirect product(C5×C491)⋊(C3×C5)
unambiguous semidirect product(C3×C5×C491)⋊C5

Splittings

Fitting, socleC3×C5×C491 ⋊ C5
derived, SylowC491 ⋊ C3×C52
HallC3×C491 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC3×C5C491⋊C5
commutator, cosocle, hypocenterC491C3×C52
FrattiniC1G
Fitting, socleC3×C5×C491C5
LCSG ▷ C491
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7365

Conjugacy classes & character table

1545 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36825, 4);