Finite Group Databasebeta

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D5×C11×D31⋊C5 #46802091

order34100
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D31⋊C5
unambiguous semidirect productD31⋊(C5×D5×C11)
unambiguous semidirect product(D5×D31)⋊(C5×C11)
unambiguous semidirect product(C5×D31⋊C5)⋊(C2×C11)
unambiguous semidirect product(D5×ΓL(1,𝔽32))⋊(C2×C11)
unambiguous semidirect product(C5⋊(D31⋊C5))⋊(C2×C11)

Splittings

Fitting, socleC5×C11×C31 ⋊ C22×C5
derivedC5×C31 ⋊ C22×C5×C11
HallC5×C11×ΓL(1,𝔽32) ⋊ C22
HallC5×ΓL(1,𝔽32) ⋊ C22×C11
HallC11×C31 ⋊ C2×C5×D5
SylowC31 ⋊ C2×C5×D5×C11

Subgroups

subgroupG/H
center, hypercenterC11D5×D31⋊C5
commutator, cosocle, hypocenterC5×C31C22×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C31C22×C5
LCSG ▷ C5×C31
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1705

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 182);