Finite Group Databasebeta

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D5×C41×C7⋊C9 #38788926

order25830
automorphism?
homologyAbelianization (H1) = C2×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productD5×C41×C7⋊C9
unambiguous semidirect productC5⋊(C2×C41×C7⋊C9)
unambiguous semidirect product(C7×D5)⋊(C9×C41)
unambiguous semidirect product(C7×D5×C41)⋊C9

Splittings

derived, HallC5×C7 ⋊ C2×C9×C41
HallC5×C41×C7⋊C9 ⋊ C2
HallC7×D5×C41 ⋊ C9
HallC5×C7×C41 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C41
HallC7×C41 ⋊ C9×D5
HallC5×C41 ⋊ C2×C7⋊C9
HallC7×D5 ⋊ C9×C41
SylowC7 ⋊ C9×D5×C41
SylowC5 ⋊ C2×C41×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C41D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C9×C41
FrattiniC3D5×ΓL(1,𝔽8)×C41
Fitting, socleC3×C5×C7×C41C2×C3
prime radicalC3×C7×D5×C41C3
cosocleC3×C5×C7C2×C3×C41
LCSG ▷ C5×C7
UCSC1 ◁ C3×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 30);