Finite Group Databasebeta

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C3×C19×D77 #22578609

order8778
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×D77
unambiguous semidirect productC11⋊(C3×D7×C19)

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C2
derived, HallC7×C11 ⋊ C2×C3×C19
HallC7×C11×C19 ⋊ C2×C3
HallC3×C11×C19 ⋊ D7
HallC3×C7×C19 ⋊ D11
HallC3×C7×C11 ⋊ C2×C19
HallC11×C19 ⋊ C3×D7
HallC7×C19 ⋊ C3×D11
HallC3×C11 ⋊ D7×C19
HallC3×C7 ⋊ C19×D11
SylowC11 ⋊ C3×D7×C19
SylowC7 ⋊ C3×C19×D11

Subgroups

subgroupG/H
center, hypercenterC3×C19D77
commutator, hypocenterC7×C11C2×C3×C19
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2
LCSG ▷ C7×C11
UCSC1 ◁ C3×C19

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D19×D77, C3×D7×C19×D11, C3×D77⋊D19, …
maximal normal subgroup ofC3×D19×D77, C3×D7×C19×D11, C3×D77⋊D19, …
maximal quotient ofC3×C19×Dic77, C2×C3×C19×D77, C9×C19×D77, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 11);