Finite Group Databasebeta

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C5×C3⋊((C211⋊C3)⋊C4) #49183994

order37980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊((C211⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C5×(C211⋊C3)⋊C4)
unambiguous semidirect product(C5×Dic633)⋊C3

Splittings

derivedC3×C211 ⋊ C3×C4×C5
HallC3×C5×C211⋊C3 ⋊ C4
HallC3×C211⋊C3 ⋊ C4×C5
HallC5×C211 ⋊ C3×Dic3
SylowC211 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D211⋊C3)
commutator, hypocenterC3×C211C3×C4×C5
FrattiniC2C5×C3⋊(D211⋊C3)
Fitting, socleC2×C3×C5×C211C2×C3
prime radicalC2×C3×C5×C211⋊C3C2
cosocleC2×C3×C211C2×C3×C5
LCSG ▷ C3×C211
UCSC1 ◁ C2×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12660

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37980, 69);