Finite Group Databasebeta

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C2×C3×C7×C101⋊C5 #35234575

order21210
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C7×C101⋊C5
unambiguous semidirect product(C2×C101)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C3×C101)⋊(C5×C7)
unambiguous semidirect product(C2×C3×C7×C101)⋊C5

Splittings

Fitting, socle, HallC2×C3×C7×C101 ⋊ C5
derived, SylowC101 ⋊ C2×C3×C5×C7
HallC3×C7×C101 ⋊ C2×C5
HallC2×C7×C101 ⋊ C3×C5
HallC7×C101 ⋊ C2×C3×C5
HallC2×C3×C101 ⋊ C5×C7
HallC3×C101 ⋊ C2×C5×C7
HallC2×C101 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C101⋊C5
commutator, cosocle, hypocenterC101C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C101C5
LCSG ▷ C101
UCSC1 ◁ C2×C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4242

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 2);