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C2×C5×D311⋊C5 #44527364

order31100
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×D311⋊C5
unambiguous semidirect productD311⋊(C2×C52)
unambiguous semidirect product(C2×D311)⋊C52
unambiguous semidirect product(C311⋊C5)⋊(C22×C5)
unambiguous semidirect product(C2×C311⋊C5)⋊(C2×C5)
unambiguous semidirect product(C2×C5×D311)⋊C5

Splittings

Fitting, socleC2×C5×C311 ⋊ C2×C5
derived, SylowC311 ⋊ C22×C52
HallC5×C311⋊C5 ⋊ C22
HallC2×D311 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC2×C5D311⋊C5
commutator, cosocle, hypocenterC311C22×C52
FrattiniC1G
Fitting, socleC2×C5×C311C2×C5
LCSG ▷ C311
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3110

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31100, 30);