Finite Group Databasebeta

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C3×C7×C11×D19 #22578604

order8778
isoclinismisoclinic class of D19
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×D19

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C2
derived, SylowC19 ⋊ C2×C3×C7×C11
HallC7×C11×C19 ⋊ C2×C3
HallC3×C11×C19 ⋊ C2×C7
HallC3×C7×C19 ⋊ C2×C11
HallC11×C19 ⋊ C2×C3×C7
HallC7×C19 ⋊ C2×C3×C11
HallC3×C19 ⋊ C2×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D19
commutator, hypocenterC19C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2
LCSG ▷ C19
UCSC1 ◁ C3×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2541 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×D11×D19, C3×C11×D7×D19, C3×D19×D77, …
maximal normal subgroup ofC3×C7×D11×D19, C3×C11×D7×D19, C3×D19×D77, …
maximal quotient ofC3×C7×C11×Dic19, C2×C3×C7×C11×D19, C7×C9×C11×D19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 6);