Finite Group Databasebeta

← Prev (#22552110) Next (#22552112) →

C5×C7×C79⋊C3 #22552111

order8295
isoclinismisoclinic class of C79⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C79⋊C3
unambiguous semidirect productC79⋊(C3×C5×C7)
unambiguous semidirect product(C5×C79)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C79 ⋊ C3
derived, SylowC79 ⋊ C3×C5×C7
HallC7×C79 ⋊ C3×C5
HallC5×C79 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7C79⋊C3
commutator, hypocenterC79C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C79C3
LCSG ▷ C79
UCSC1 ◁ C5×C7

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C7×C79⋊C3, C5×C7×D79⋊C3, C5×D7×C79⋊C3, …
maximal normal subgroup ofC2×C5×C7×C79⋊C3, C5×C7×D79⋊C3, C5×D7×C79⋊C3, …
maximal quotient ofC2×C5×C7×C79⋊C3, C5×C7×C79⋊C9, C3×C5×C7×C79⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8295, 2);