Finite Group Databasebeta

← Prev (#34038374) Next (#34038376) →

C4×C13⋊(C112⋊C3) #34038375

order18876
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productC4×C13⋊(C112⋊C3)
unambiguous semidirect product(C4×C13)⋊(C112⋊C3)
unambiguous semidirect product(C4×C112)⋊(C13⋊C3)

Splittings

Fitting, HallC4×C112×C13 ⋊ C3
derived, HallC112×C13 ⋊ C3×C4
HallC4×C112 ⋊ C13⋊C3
SylowC112 ⋊ C4×C13⋊C3
HallC4×C13 ⋊ C112⋊C3
SylowC13 ⋊ C4×C112⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C13⋊(C112⋊C3)
commutator, hypocenterC112×C13C3×C4
FrattiniC2C2×C13⋊(C112⋊C3)
FittingC4×C112×C13C3
socle, cosocleC2×C112×C13C2×C3
prime radicalC2×C13⋊(C112⋊C3)C2
LCSG ▷ C112×C13
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1716

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 57);