Finite Group Databasebeta

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C3×C5×Dic43⋊C7 #31825347

order18060
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic43⋊C7
unambiguous semidirect product(C3×Dic43)⋊(C5×C7)
unambiguous semidirect product(C3×C5×Dic43)⋊C7

Splittings

derived, SylowC43 ⋊ C3×C4×C5×C7
HallC3×C5×C43⋊C7 ⋊ C4
HallC3×C5×Dic43 ⋊ C7
HallC5×C43⋊C7 ⋊ C3×C4
HallC3×C43⋊C7 ⋊ C4×C5
HallC5×Dic43 ⋊ C3×C7
HallC3×C5×C43 ⋊ C4×C7
HallC3×Dic43 ⋊ C5×C7
HallC43⋊C7 ⋊ C3×C4×C5
HallC5×C43 ⋊ C3×C4×C7
HallDic43 ⋊ C3×C5×C7
HallC3×C43 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D43⋊C7
commutator, hypocenterC43C3×C4×C5×C7
FrattiniC2C3×C5×D43⋊C7
Fitting, socleC2×C3×C5×C43C2×C7
prime radicalC2×C3×C5×C43⋊C7C2
cosocleC2×C43C2×C3×C5×C7
LCSG ▷ C43
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2580

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 23);