Finite Group Databasebeta

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C4×C13×C67⋊C9 #44535566

order31356
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, SylowC67 ⋊ C4×C9×C13
HallC4×C13×C67 ⋊ C9
HallC13×C67 ⋊ C4×C9
HallC4×C67 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4×C13C67⋊C3
commutator, hypocenterC67C4×C9×C13
FrattiniC2×C3C2×C13×C67⋊C3
FittingC3×C4×C13×C67C3
socle, prime radicalC2×C3×C13×C67C2×C3
cosocleC2×C3×C67C2×C3×C13
LCSG ▷ C67
UCSC1 ◁ C3×C4×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31356

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 2);