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C7×C9×Dic131 #45682591

order33012
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic131
unambiguous semidirect productC131⋊(C4×C7×C9)

Splittings

derived, SylowC131 ⋊ C4×C7×C9
HallC7×C9×C131 ⋊ C4
HallC9×C131 ⋊ C4×C7
HallC7×C131 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D131
commutator, hypocenterC131C4×C7×C9
FrattiniC2×C3C3×C7×D131
FittingC2×C7×C9×C131C2
socle, prime radicalC2×C3×C7×C131C2×C3
cosocleC2×C3×C131C2×C3×C7
LCSG ▷ C131
UCSC1 ◁ C2×C7×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33012

Conjugacy classes & character table

8442 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33012, 3);