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C2×C23×D41⋊C5 #34038203

order18860
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D41⋊C5
unambiguous semidirect productD41⋊(C2×C5×C23)
unambiguous semidirect product(C2×D41)⋊(C5×C23)
unambiguous semidirect product(C41⋊C5)⋊(C22×C23)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C23)
unambiguous semidirect product(C2×C23×D41)⋊C5

Splittings

Fitting, socleC2×C23×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C5×C23
HallC23×C41⋊C5 ⋊ C22
HallC2×C23×D41 ⋊ C5
HallC23×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C22×C23
HallC2×D41 ⋊ C5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23D41⋊C5
commutator, cosocle, hypocenterC41C22×C5×C23
FrattiniC1G
Fitting, socleC2×C23×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1886

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18860, 17);