Finite Group Databasebeta

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C101×D105 #35234591

order21210
automorphism?
homologyAbelianization (H1) = C2×C101 · Schur multiplier (H2) = C1

Aliases

direct productC101×D105
unambiguous semidirect productC3⋊(D35×C101)
unambiguous semidirect productC5⋊(D21×C101)
unambiguous semidirect productC7⋊(D15×C101)

Splittings

Fitting, socle, HallC3×C5×C7×C101 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C101
HallC5×C7×C101 ⋊ D3
HallC3×C7×C101 ⋊ D5
HallC3×C5×C101 ⋊ D7
HallC7×C101 ⋊ D15
HallC5×C101 ⋊ D21
HallC3×C101 ⋊ D35
HallC5×C7 ⋊ D3×C101
HallC3×C7 ⋊ D5×C101
HallC3×C5 ⋊ D7×C101
SylowC7 ⋊ D15×C101
SylowC5 ⋊ D21×C101
SylowC3 ⋊ D35×C101

Subgroups

subgroupG/H
center, hypercenterC101D105
commutator, cosocle, hypocenterC3×C5×C7C2×C101
FrattiniC1G
Fitting, socleC3×C5×C7×C101C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C101

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10605

Conjugacy classes & character table

5454 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 18);