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C3⋊(C7⋊(D101⋊C5)) #35234599

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

Aliases

unambiguous semidirect productC3⋊(C7⋊(D101⋊C5))
unambiguous semidirect productC7⋊(C3⋊(D101⋊C5))
unambiguous semidirect product(C101⋊C5)⋊D21
unambiguous semidirect productD2121⋊C5

Splittings

Fitting, socle, derived, HallC3×C7×C101 ⋊ C2×C5
HallC3×C7×C101⋊C5 ⋊ C2
HallD2121 ⋊ C5
HallC7×C101⋊C5 ⋊ D3
HallC3×C101⋊C5 ⋊ D7
HallC7×C101 ⋊ C5×D3
HallC101⋊C5 ⋊ D21
HallC3×C101 ⋊ C5×D7
SylowC101 ⋊ C5×D21
HallC3×C7 ⋊ D101⋊C5
SylowC7 ⋊ C3⋊(D101⋊C5)
SylowC3 ⋊ C7⋊(D101⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C101C2×C5
LCSG ▷ C3×C7×C101
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2121

Polycyclic presentation:

2,3,5,7,101|b^a=b^2,d^a=d^6,e^a=e^100,e^c=e^95

Conjugacy classes & character table

270 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 26);