Finite Group Databasebeta

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C112×C22⋊(C13⋊C3) #34038470

order18876
automorphism?
homologyAbelianization (H1) = C3×C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC112×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C112×C13⋊C3)
unambiguous semidirect productC13⋊(C112×A4)
unambiguous semidirect product(C22×C11)⋊(C11×C13⋊C3)
unambiguous semidirect product(C11×C13)⋊(C11×A4)

Splittings

Fitting, socle, HallC22×C112×C13 ⋊ C3
derived, HallC22×C13 ⋊ C3×C112
HallC112×C13 ⋊ A4
HallC22×C112 ⋊ C13⋊C3
SylowC13 ⋊ C112×A4
SylowC22 ⋊ C112×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC112C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C112
FrattiniC1G
Fitting, socleC22×C112×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C112

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6292

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 152);