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C13×Dic9×C67 #44535573

order31356
automorphism?
homologyAbelianization (H1) = C4×C13×C67 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic9×C67
unambiguous semidirect productC9⋊(C4×C13×C67)

Splittings

derived, SylowC9 ⋊ C4×C13×C67
HallC9×C13×C67 ⋊ C4
HallC9×C67 ⋊ C4×C13
HallC9×C13 ⋊ C4×C67

Subgroups

subgroupG/H
center, hypercenterC2×C13×C67D9
commutator, hypocenterC9C4×C13×C67
FrattiniC2×C3D3×C13×C67
FittingC2×C9×C13×C67C2
socle, prime radicalC2×C3×C13×C67D3
cosocleC2×C9C2×C13×C67
LCSG ▷ C9
UCSC1 ◁ C2×C13×C67

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31356

Conjugacy classes & character table

10452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 9);