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C3⋊D21×C41⋊C5 #38788952

order25830
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3⋊D21×C41⋊C5
unambiguous semidirect productC3⋊(D21×C41⋊C5)
unambiguous semidirect productC7⋊(C3⋊D3×C41⋊C5)
unambiguous semidirect product(C41×C3⋊D21)⋊C5

Splittings

Fitting, socle, derived, HallC32×C7×C41 ⋊ C2×C5
HallC32×C7×C41⋊C5 ⋊ C2
HallC41×C3⋊D21 ⋊ C5
HallC32×C41⋊C5 ⋊ D7
HallC7×C41⋊C5 ⋊ C3⋊D3
HallC32×C41 ⋊ C5×D7
HallC7×C41 ⋊ C5×C3⋊D3
HallC32×C7 ⋊ C2×C41⋊C5
SylowC41 ⋊ C5×C3⋊D21
SylowC32 ⋊ D7×C41⋊C5
SylowC7 ⋊ C3⋊D3×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C41C2×C5
LCSG ▷ C32×C7×C41
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 56);