Finite Group Databasebeta

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C9×C11×Dic77 #44478909

order30492
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×Dic77
unambiguous semidirect productC11⋊(C9×C11×Dic7)

Splittings

derivedC7×C11 ⋊ C4×C9×C11
HallC7×C9×C112 ⋊ C4
HallC9×C112 ⋊ Dic7
HallC7×C112 ⋊ C4×C9
SylowC112 ⋊ C9×Dic7
HallC7×C9 ⋊ C11×Dic11
SylowC7 ⋊ C9×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D77
commutator, hypocenterC7×C11C4×C9×C11
FrattiniC2×C3C3×C11×D77
FittingC2×C7×C9×C112C2
socle, prime radicalC2×C3×C7×C112C2×C3
cosocleC2×C3×C7×C11C2×C3×C11
LCSG ▷ C7×C11
UCSC1 ◁ C2×C9×C11

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 132);