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C19⋊C3×D77 #22578639

order8778
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC19⋊C3×D77
unambiguous semidirect productC11⋊(D7×C19⋊C3)

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C2×C3
HallC7×C11×C19⋊C3 ⋊ C2
HallC19×D77 ⋊ C3
HallC11×C19⋊C3 ⋊ D7
HallC7×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C3×D7
HallC7×C19 ⋊ C3×D11
HallC7×C11 ⋊ C2×C19⋊C3
SylowC19 ⋊ C3×D77
SylowC11 ⋊ D7×C19⋊C3
SylowC7 ⋊ D11×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C11×C19C2×C3
LCSG ▷ C7×C11×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×D77, ((C19⋊C3)⋊D7)⋊D11, D7×D11×C19⋊C3, …
maximal normal subgroup ofD19⋊C3×D77, ((C19⋊C3)⋊D7)⋊D11, D7×D11×C19⋊C3, …
maximal quotient ofC19⋊C3×Dic77, C2×C19⋊C3×D77, D77×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 41);