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C5×C7×C181⋊C5 #44540008

order31675
automorphism?
homologyAbelianization (H1) = C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C181⋊C5
unambiguous semidirect productC181⋊(C52×C7)
unambiguous semidirect product(C5×C181)⋊(C5×C7)
unambiguous semidirect product(C7×C181)⋊C52
unambiguous semidirect product(C5×C7×C181)⋊C5

Splittings

Fitting, socleC5×C7×C181 ⋊ C5
derived, SylowC181 ⋊ C52×C7
HallC7×C181 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C7C181⋊C5
commutator, cosocle, hypocenterC181C52×C7
FrattiniC1G
Fitting, socleC5×C7×C181C5
LCSG ▷ C181
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6335

Conjugacy classes & character table

1435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31675, 4);