Finite Group Databasebeta

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C9×C37×Dic23 #44499601

order30636
automorphism?
homologyAbelianization (H1) = C4×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC9×C37×Dic23
unambiguous semidirect productC23⋊(C4×C9×C37)

Splittings

derived, SylowC23 ⋊ C4×C9×C37
HallC9×C23×C37 ⋊ C4
HallC23×C37 ⋊ C4×C9
HallC9×C23 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC2×C9×C37D23
commutator, hypocenterC23C4×C9×C37
FrattiniC2×C3C3×C37×D23
FittingC2×C9×C23×C37C2
socle, prime radicalC2×C3×C23×C37C2×C3
cosocleC2×C3×C23C2×C3×C37
LCSG ▷ C23
UCSC1 ◁ C2×C9×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30636

Conjugacy classes & character table

8658 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 4);