Finite Group Databasebeta

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C2×C7×C11×C19⋊C3 #22578600

order8778
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C11×C19⋊C3
unambiguous semidirect product(C2×C19)⋊(C3×C7×C11)
unambiguous semidirect product(C2×C11×C19)⋊(C3×C7)

Splittings

Fitting, socle, HallC2×C7×C11×C19 ⋊ C3
derived, SylowC19 ⋊ C2×C3×C7×C11
HallC7×C11×C19 ⋊ C2×C3
HallC2×C11×C19 ⋊ C3×C7
HallC2×C7×C19 ⋊ C3×C11
HallC11×C19 ⋊ C2×C3×C7
HallC7×C19 ⋊ C2×C3×C11
HallC2×C19 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C19⋊C3
commutator, hypocenterC19C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C19C3
LCSG ▷ C19
UCSC1 ◁ C2×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×C11×C19⋊C3, C7×C11×(C19⋊C3)⋊C4, C7×Dic11×C19⋊C3, …
maximal normal subgroup ofC4×C7×C11×C19⋊C3, C7×C11×(C19⋊C3)⋊C4, C7×Dic11×C19⋊C3, …
maximal quotient ofC4×C7×C11×C19⋊C3, C22×C7×C11×C19⋊C3, C2×C7×C11×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 2);