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C19×D231 #22578617

order8778
isoclinismisoclinic class of D231
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D231
unambiguous semidirect productC3⋊(C19×D77)
unambiguous semidirect productC7⋊(C19×D33)
unambiguous semidirect productC11⋊(C19×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C19
HallC7×C11×C19 ⋊ D3
HallC3×C11×C19 ⋊ D7
HallC3×C7×C19 ⋊ D11
HallC11×C19 ⋊ D21
HallC7×C19 ⋊ D33
HallC7×C11 ⋊ D3×C19
HallC3×C19 ⋊ D77
HallC3×C11 ⋊ D7×C19
HallC3×C7 ⋊ C19×D11
SylowC11 ⋊ C19×D21
SylowC7 ⋊ C19×D33
SylowC3 ⋊ C19×D77

Subgroups

subgroupG/H
center, hypercenterC19D231
commutator, hypocenterC3×C7×C11C2×C19
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2223 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19×D231, C19×D11×D21, D209⋊D21, …
maximal normal subgroup ofD19×D231, C19×D11×D21, D209⋊D21, …
maximal quotient ofC19×Dic231, C2×C19×D231, C19×D693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 19);