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C5×D77⋊D23 #47978440

order35420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D77⋊D23
unambiguous semidirect productD161⋊(C5×D11)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C22
derived, HallC7×C11×C23 ⋊ C22×C5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC11×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C2×C5×D11
HallC5×C23 ⋊ D7×D11
HallC7×C11 ⋊ C2×C5×D23
HallC5×C11 ⋊ D7×D23
HallC5×C7 ⋊ D11×D23
SylowC23 ⋊ C5×D7×D11
SylowC11 ⋊ C5×D7×D23
SylowC7 ⋊ C5×D11×D23

Subgroups

subgroupG/H
center, hypercenterC5D77⋊D23
commutator, cosocle, hypocenterC7×C11×C23C22×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C23C22
LCSG ▷ C7×C11×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

2375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 74);