Finite Group Databasebeta

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C7×C9×C11⋊Dic11 #44478907

order30492
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C11

Aliases

direct productC7×C9×C11⋊Dic11
unambiguous semidirect productC11⋊(C7×C9×Dic11)

Splittings

derived, SylowC112 ⋊ C4×C7×C9
HallC7×C9×C112 ⋊ C4
HallC9×C112 ⋊ C4×C7
HallC7×C112 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9C11⋊D11
commutator, hypocenterC112C4×C7×C9
FrattiniC2×C3C3×C7×C11⋊D11
FittingC2×C7×C9×C112C2
socle, prime radicalC2×C3×C7×C112C2×C3
cosocleC2×C3×C112C2×C3×C7
LCSG ▷ C112
UCSC1 ◁ C2×C7×C9

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30492

Conjugacy classes & character table

7812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 130);