Finite Group Databasebeta

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C112×Dic13⋊C3 #34038360

order18876
automorphism?
homologyAbelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC112×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C112)
unambiguous semidirect product(C11×Dic13)⋊(C3×C11)

Splittings

derived, SylowC13 ⋊ C3×C4×C112
HallC112×Dic13 ⋊ C3
HallC112×C13⋊C3 ⋊ C4
HallC112×C13 ⋊ C3×C4
HallDic13 ⋊ C3×C112
HallC13⋊C3 ⋊ C4×C112

Subgroups

subgroupG/H
center, hypercenterC2×C112D13⋊C3
commutator, hypocenterC13C3×C4×C112
FrattiniC2C112×D13⋊C3
Fitting, socleC2×C112×C13C2×C3
prime radicalC2×C112×C13⋊C3C2
cosocleC2×C13C2×C3×C112
LCSG ▷ C13
UCSC1 ◁ C2×C112

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6292

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 42);