Finite Group Databasebeta

← Prev (#38764111) Next (#38764113) →

C7×Dic9×C101 #38764112

order25452
automorphism?
homologyAbelianization (H1) = C4×C7×C101 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic9×C101
unambiguous semidirect productC9⋊(C4×C7×C101)

Splittings

derived, SylowC9 ⋊ C4×C7×C101
HallC7×C9×C101 ⋊ C4
HallC9×C101 ⋊ C4×C7
HallC7×C9 ⋊ C4×C101

Subgroups

subgroupG/H
center, hypercenterC2×C7×C101D9
commutator, hypocenterC9C4×C7×C101
FrattiniC2×C3D3×C7×C101
FittingC2×C7×C9×C101C2
socle, prime radicalC2×C3×C7×C101D3
cosocleC2×C9C2×C7×C101
LCSG ▷ C9
UCSC1 ◁ C2×C7×C101

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25452

Conjugacy classes & character table

8484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25452, 6);