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C52×C7×C13⋊C3 #20291983

order6825
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×C7×C13⋊C3
unambiguous semidirect productC13⋊(C3×C52×C7)
unambiguous semidirect product(C5×C13)⋊(C3×C5×C7)

Splittings

Fitting, socle, HallC52×C7×C13 ⋊ C3
derived, SylowC13 ⋊ C3×C52×C7
HallC52×C13 ⋊ C3×C7
HallC7×C13 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC52×C7C13⋊C3
commutator, hypocenterC13C3×C52×C7
FrattiniC1G
Fitting, socleC52×C7×C13C3
LCSG ▷ C13
UCSC1 ◁ C52×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC52×C7×D13⋊C3, C52×(C13⋊C3)⋊D7, C52×D7×C13⋊C3, …
maximal normal subgroup ofC52×C7×D13⋊C3, C52×(C13⋊C3)⋊D7, C52×D7×C13⋊C3, …
maximal quotient ofC2×C52×C7×C13⋊C3, C52×C7×C13⋊C9, C3×C52×C7×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6825, 15);