Finite Group Databasebeta

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C11×D399 #22578616

order8778
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D399
unambiguous semidirect productC3⋊(C11×D133)
unambiguous semidirect productC7⋊(C11×D57)
unambiguous semidirect productC19⋊(C11×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C2
derived, HallC3×C7×C19 ⋊ C2×C11
HallC7×C11×C19 ⋊ D3
HallC3×C11×C19 ⋊ D7
HallC3×C7×C11 ⋊ D19
HallC11×C19 ⋊ D21
HallC7×C19 ⋊ D3×C11
HallC7×C11 ⋊ D57
HallC3×C19 ⋊ C11×D7
HallC3×C11 ⋊ D133
HallC3×C7 ⋊ C11×D19
SylowC19 ⋊ C11×D21
SylowC7 ⋊ C11×D57
SylowC3 ⋊ C11×D133

Subgroups

subgroupG/H
center, hypercenterC11D399
commutator, hypocenterC3×C7×C19C2×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2
LCSG ▷ C3×C7×C19
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2211 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D19×D21, D11×D399, D209⋊D21, …
maximal normal subgroup ofC11×D19×D21, D11×D399, D209⋊D21, …
maximal quotient ofC11×Dic399, C2×C11×D399, C11×D1197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 18);