Finite Group Databasebeta

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C2×C3×D23⋊C121 #45688952

order33396
automorphism?
homologyAbelianization (H1) = C22×C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D23⋊C121
unambiguous semidirect productD23⋊(C2×C3×C121)
unambiguous semidirect product(C2×D23)⋊(C3×C121)
unambiguous semidirect product(C2×C3×D23)⋊C121
unambiguous semidirect product(C23⋊C121)⋊(C22×C3)
unambiguous semidirect product(C2×C23⋊C121)⋊(C2×C3)

Splittings

derived, SylowC23 ⋊ C22×C3×C121
HallC3×C23⋊C121 ⋊ C22
HallC23⋊C121 ⋊ C22×C3
HallC2×C3×D23 ⋊ C121
HallC2×D23 ⋊ C3×C121
HallC3×C23 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11AGL(1,𝔽23)
commutator, hypocenterC23C22×C3×C121
FrattiniC11C2×C3×AGL(1,𝔽23)
Fitting, socleC2×C3×C11×C23C2×C11
prime radicalC2×C3×C11×D23C11
cosocleC11×C23C22×C3×C11
LCSG ▷ C23
UCSC1 ◁ C2×C3×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16698

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 16);