Finite Group Databasebeta

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C2×C32×C7×C41⋊C5 #38788968

order25830
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C32×C7×C41⋊C5
unambiguous semidirect product(C2×C41)⋊(C32×C5×C7)
unambiguous semidirect product(C2×C3×C41)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C32×C41)⋊(C5×C7)
unambiguous semidirect product(C2×C32×C7×C41)⋊C5

Splittings

Fitting, socle, HallC2×C32×C7×C41 ⋊ C5
derived, SylowC41 ⋊ C2×C32×C5×C7
HallC32×C7×C41 ⋊ C2×C5
HallC2×C32×C41 ⋊ C5×C7
HallC2×C7×C41 ⋊ C32×C5
HallC32×C41 ⋊ C2×C5×C7
HallC7×C41 ⋊ C2×C32×C5
HallC2×C41 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C7C41⋊C5
commutator, cosocle, hypocenterC41C2×C32×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C41C5
LCSG ▷ C41
UCSC1 ◁ C2×C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5166

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 72);