Finite Group Databasebeta

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C3×D7×C101⋊C5 #35234594

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

Aliases

direct productC3×D7×C101⋊C5
unambiguous semidirect product(C3×D7×C101)⋊C5

Splittings

Fitting, socle, HallC3×C7×C101 ⋊ C2×C5
derived, HallC7×C101 ⋊ C2×C3×C5
HallC3×C7×C101⋊C5 ⋊ C2
HallC3×D7×C101 ⋊ C5
HallC7×C101⋊C5 ⋊ C2×C3
HallD7×C101 ⋊ C3×C5
HallC3×C101 ⋊ C5×D7
SylowC101 ⋊ C3×C5×D7
HallC3×C7 ⋊ C2×C101⋊C5
SylowC7 ⋊ C2×C3×C101⋊C5

Subgroups

subgroupG/H
center, hypercenterC3D7×C101⋊C5
commutator, cosocle, hypocenterC7×C101C2×C3×C5
FrattiniC1G
Fitting, socleC3×C7×C101C2×C5
LCSG ▷ C7×C101
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2121

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 21);