Finite Group Databasebeta

← Prev (#44535566) Next (#44535568) →

C4×C67×C13⋊C9 #44535567

order31356
automorphism?
homologyAbelianization (H1) = C4×C9×C67 · Schur multiplier (H2) = C1

Aliases

direct productC4×C67×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C9×C67)

Splittings

derived, SylowC13 ⋊ C4×C9×C67
HallC4×C13×C67 ⋊ C9
HallC13×C67 ⋊ C4×C9
HallC4×C13 ⋊ C9×C67

Subgroups

subgroupG/H
center, hypercenterC3×C4×C67C13⋊C3
commutator, hypocenterC13C4×C9×C67
FrattiniC2×C3C2×C13⋊C3×C67
FittingC3×C4×C13×C67C3
socle, prime radicalC2×C3×C13×C67C2×C3
cosocleC2×C3×C13C2×C3×C67
LCSG ▷ C13
UCSC1 ◁ C3×C4×C67

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31356

Conjugacy classes & character table

5628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 3);