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C23×C22⋊(C43⋊C3) #26045147

order11868
automorphism?
homologyAbelianization (H1) = C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×C22⋊(C43⋊C3)
unambiguous semidirect productC22⋊(C23×C43⋊C3)
unambiguous semidirect productC43⋊(A4×C23)
unambiguous semidirect product(C22×C23)⋊(C43⋊C3)
unambiguous semidirect product(C23×C43)⋊A4

Splittings

Fitting, socle, HallC22×C23×C43 ⋊ C3
derived, HallC22×C43 ⋊ C3×C23
HallC23×C43 ⋊ A4
HallC22×C23 ⋊ C43⋊C3
SylowC43 ⋊ A4×C23
SylowC22 ⋊ C23×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC23C22⋊(C43⋊C3)
commutator, cosocle, hypocenterC22×C43C3×C23
FrattiniC1G
Fitting, socleC22×C23×C43C3
LCSG ▷ C22×C43
UCSC1 ◁ C23

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C23×C43⋊C3, C3×C23×C22⋊(C43⋊C3)
maximal normal subgroup ofA4×C23×C43⋊C3, C3×C23×C22⋊(C43⋊C3)
maximal quotient ofC23×C22⋊(C43⋊C9), C3×C23×C22⋊(C43⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11868, 25);