Finite Group Databasebeta

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C11×Dic181⋊C3 #37560662

order23892
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic181⋊C3
unambiguous semidirect productDic181⋊(C3×C11)
unambiguous semidirect product(C11×Dic181)⋊C3

Splittings

derived, SylowC181 ⋊ C3×C4×C11
HallC11×Dic181 ⋊ C3
HallC11×C181⋊C3 ⋊ C4
HallC11×C181 ⋊ C3×C4
HallDic181 ⋊ C3×C11
HallC181⋊C3 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D181⋊C3
commutator, hypocenterC181C3×C4×C11
FrattiniC2C11×D181⋊C3
Fitting, socleC2×C11×C181C2×C3
prime radicalC2×C11×C181⋊C3C2
cosocleC2×C181C2×C3×C11
LCSG ▷ C181
UCSC1 ◁ C2×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7964

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23892, 10);