Finite Group Databasebeta

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C3×C4×C601⋊C5 #49115125

order36060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C601⋊C5
unambiguous semidirect product(C3×C4×C601)⋊C5

Splittings

Fitting, HallC3×C4×C601 ⋊ C5
derived, SylowC601 ⋊ C3×C4×C5
HallC4×C601 ⋊ C3×C5
HallC3×C601 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4C601⋊C5
commutator, hypocenterC601C3×C4×C5
FrattiniC2C2×C3×C601⋊C5
FittingC3×C4×C601C5
socleC2×C3×C601C2×C5
prime radicalC2×C3×C601⋊C5C2
cosocleC2×C601C2×C3×C5
LCSG ▷ C601
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7212

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36060, 2);