Finite Group Databasebeta

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C4×C19⋊(C112⋊C3) #42119957

order27588
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productC4×C19⋊(C112⋊C3)
unambiguous semidirect product(C4×C19)⋊(C112⋊C3)
unambiguous semidirect product(C4×C112)⋊(C19⋊C3)

Splittings

Fitting, HallC4×C112×C19 ⋊ C3
derived, HallC112×C19 ⋊ C3×C4
HallC4×C112 ⋊ C19⋊C3
SylowC112 ⋊ C4×C19⋊C3
HallC4×C19 ⋊ C112⋊C3
SylowC19 ⋊ C4×C112⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C19⋊(C112⋊C3)
commutator, hypocenterC112×C19C3×C4
FrattiniC2C2×C19⋊(C112⋊C3)
FittingC4×C112×C19C3
socle, cosocleC2×C112×C19C2×C3
prime radicalC2×C19⋊(C112⋊C3)C2
LCSG ▷ C112×C19
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

3076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 49);