Finite Group Databasebeta

← Prev (#15692810) Next (#15692812) →

C3×C7×A4×C13 #15692811

order3276
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C7×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×A4×C13
unambiguous semidirect productC22⋊(C32×C7×C13)
unambiguous semidirect product(C22×C3)⋊(C3×C7×C13)

Splittings

Fitting, socleC22×C3×C7×C13 ⋊ C3
derived, SylowC22 ⋊ C32×C7×C13
HallC22×C7×C13 ⋊ C32
HallC22×C13 ⋊ C32×C7
HallC22×C7 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C7×C13A4
commutator, cosocle, hypocenterC22C32×C7×C13
FrattiniC1G
Fitting, socleC22×C3×C7×C13C3
LCSG ▷ C22
UCSC1 ◁ C3×C7×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1092

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C7×A4×C13, C3×C7×C13×A5, C3×A4×C13×C49, …
maximal normal subgroup ofC3×C5×C7×A4×C13, C3×A4×C13×C49, C3×C72×A4×C13, …
maximal quotient ofC3×C5×C7×A4×C13, C3×A4×C13×C49, C7×A4×C13×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3276, 252);