Finite Group Databasebeta

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C4×C5×C113⋊C7 #30629080

order15820
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C113⋊C7
unambiguous semidirect product(C4×C113)⋊(C5×C7)
unambiguous semidirect product(C4×C5×C113)⋊C7

Splittings

Fitting, HallC4×C5×C113 ⋊ C7
derived, SylowC113 ⋊ C4×C5×C7
HallC5×C113 ⋊ C4×C7
HallC4×C113 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC4×C5C113⋊C7
commutator, hypocenterC113C4×C5×C7
FrattiniC2C2×C5×C113⋊C7
FittingC4×C5×C113C7
socleC2×C5×C113C2×C7
prime radicalC2×C5×C113⋊C7C2
cosocleC2×C113C2×C5×C7
LCSG ▷ C113
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2260

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15820, 2);