Finite Group Databasebeta

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C4×C49×C19⋊C3 #26013752

order11172
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC4×C49×C19⋊C3
unambiguous semidirect product(C4×C19)⋊(C3×C49)

Splittings

Fitting, HallC4×C19×C49 ⋊ C3
derived, SylowC19 ⋊ C3×C4×C49
HallC19×C49 ⋊ C3×C4
HallC4×C19 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC4×C49C19⋊C3
commutator, hypocenterC19C3×C4×C49
FrattiniC2×C7C2×C7×C19⋊C3
FittingC4×C19×C49C3
socle, cosocleC2×C7×C19C2×C3×C7
prime radicalC2×C7×C19⋊C3C2×C7
LCSG ▷ C19
UCSC1 ◁ C4×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C49×#4296, C4×#22552696, C4×#22552697, …
maximal normal subgroup ofC4×C49×#4296, C4×#22552696, C4×#22552697, …
maximal quotient ofC4×C49×#4294, Dic3×C49×C19⋊C3, C3×C4×C49×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 14);