Finite Group Databasebeta

← Prev (#27159164) Next (#27159166) →

C4×C17×C61⋊C3 #27159165

order12444
isoclinismisoclinic class of C61⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C61⋊C3
unambiguous semidirect product(C4×C61)⋊(C3×C17)
unambiguous semidirect product(C4×C17×C61)⋊C3

Splittings

Fitting, HallC4×C17×C61 ⋊ C3
derived, SylowC61 ⋊ C3×C4×C17
HallC17×C61 ⋊ C3×C4
HallC4×C61 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C61⋊C3
commutator, hypocenterC61C3×C4×C17
FrattiniC2C2×C17×C61⋊C3
FittingC4×C17×C61C3
socleC2×C17×C61C2×C3
prime radicalC2×C17×C61⋊C3C2
cosocleC2×C61C2×C3×C17
LCSG ▷ C61
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic3×C17×C61⋊C3, C3×C4×C17×C61⋊C3
maximal normal subgroup ofC3×C4×C17×C61⋊C3
maximal quotient ofC4×C17×C61⋊C9, Dic3×C17×C61⋊C3, C3×C4×C17×C61⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12444, 2);