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C7⋊C9×D41⋊C5 #38788930

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7⋊C9×D41⋊C5
unambiguous semidirect productD41⋊(C5×C7⋊C9)
unambiguous semidirect product(C41⋊C5)⋊(C2×C7⋊C9)
unambiguous semidirect product(C7×D41⋊C5)⋊C9
unambiguous semidirect product(C7⋊C9×D41)⋊C5

Splittings

derived, HallC7×C41 ⋊ C2×C5×C9
HallC7⋊C9×C41⋊C5 ⋊ C2
HallC7⋊C9×D41 ⋊ C5
HallC7×D41⋊C5 ⋊ C9
HallC41×C7⋊C9 ⋊ C2×C5
HallC7×C41⋊C5 ⋊ C2×C9
HallC7×D41 ⋊ C5×C9
HallC41⋊C5 ⋊ C2×C7⋊C9
HallD41 ⋊ C5×C7⋊C9
SylowC41 ⋊ C2×C5×C7⋊C9
SylowC7 ⋊ C9×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC3ΓL(1,𝔽8)×D41⋊C5
commutator, hypocenterC7×C41C2×C5×C9
Fitting, socle, cosocleC3×C7×C41C2×C3×C5
prime radicalC3×C7×D41⋊C5C3
LCSG ▷ C7×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 34);