Finite Group Databasebeta

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C3×C4×C5×C61⋊C5 #32912973

order18300
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C4×C5×C61⋊C5
unambiguous semidirect product(C3×C4×C61)⋊C52
unambiguous semidirect product(C3×C4×C5×C61)⋊C5

Splittings

FittingC3×C4×C5×C61 ⋊ C5
derived, SylowC61 ⋊ C3×C4×C52
HallC3×C4×C61 ⋊ C52
HallC4×C61 ⋊ C3×C52
HallC3×C61 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C61⋊C5
commutator, hypocenterC61C3×C4×C52
FrattiniC2C2×C3×C5×C61⋊C5
FittingC3×C4×C5×C61C5
socleC2×C3×C5×C61C2×C5
prime radicalC2×C3×C5×C61⋊C5C2
cosocleC2×C61C2×C3×C52
LCSG ▷ C61
UCSC1 ◁ C3×C4×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3660

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 96);