Finite Group Databasebeta

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C52×C197⋊C7 #46828119

order34475
automorphism?
homologyAbelianization (H1) = C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×C197⋊C7
unambiguous semidirect productC197⋊(C52×C7)
unambiguous semidirect product(C5×C197)⋊(C5×C7)
unambiguous semidirect product(C52×C197)⋊C7

Splittings

Fitting, socle, HallC52×C197 ⋊ C7
derived, SylowC197 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC52C197⋊C7
commutator, cosocle, hypocenterC197C52×C7
FrattiniC1G
Fitting, socleC52×C197C7
LCSG ▷ C197
UCSC1 ◁ C52

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4925

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34475, 4);