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C17×C22⋊(C61⋊C3) #27159206

order12444
automorphism?
homologyAbelianization (H1) = C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×C22⋊(C61⋊C3)
unambiguous semidirect productC22⋊(C17×C61⋊C3)
unambiguous semidirect productC61⋊(A4×C17)
unambiguous semidirect product(C22×C17)⋊(C61⋊C3)
unambiguous semidirect product(C17×C61)⋊A4

Splittings

Fitting, socle, HallC22×C17×C61 ⋊ C3
derived, HallC22×C61 ⋊ C3×C17
HallC17×C61 ⋊ A4
HallC22×C17 ⋊ C61⋊C3
SylowC61 ⋊ A4×C17
SylowC22 ⋊ C17×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C22⋊(C61⋊C3)
commutator, cosocle, hypocenterC22×C61C3×C17
FrattiniC1G
Fitting, socleC22×C17×C61C3
LCSG ▷ C22×C61
UCSC1 ◁ C17

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C17×C61⋊C3, C3×C17×C22⋊(C61⋊C3)
maximal normal subgroup ofA4×C17×C61⋊C3, C3×C17×C22⋊(C61⋊C3)
maximal quotient ofC17×C22⋊(C61⋊C9), C3×C17×C22⋊(C61⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12444, 43);