Finite Group Databasebeta

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C2×C5×C41×C7⋊C9 #38788899

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C41×C7⋊C9
unambiguous semidirect product(C2×C7)⋊(C5×C9×C41)
unambiguous semidirect product(C2×C5×C7)⋊(C9×C41)
unambiguous semidirect product(C2×C5×C7×C41)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C41
HallC2×C5×C7×C41 ⋊ C9
HallC5×C7×C41 ⋊ C2×C9
HallC2×C7×C41 ⋊ C5×C9
HallC7×C41 ⋊ C2×C5×C9
HallC2×C5×C7 ⋊ C9×C41
HallC5×C7 ⋊ C2×C9×C41
HallC2×C7 ⋊ C5×C9×C41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C41ΓL(1,𝔽8)
commutator, hypocenterC7C2×C5×C9×C41
FrattiniC3C2×C5×ΓL(1,𝔽8)×C41
Fitting, socle, prime radicalC2×C3×C5×C7×C41C3
cosocleC3×C7C2×C3×C5×C41
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25830

Conjugacy classes & character table

6150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 3);