Finite Group Databasebeta

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C7×C9×Dic127 #44544626

order32004
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic127

Splittings

derived, SylowC127 ⋊ C4×C7×C9
HallC7×C9×C127 ⋊ C4
HallC9×C127 ⋊ C4×C7
HallC7×C127 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D127
commutator, hypocenterC127C4×C7×C9
FrattiniC2×C3C3×C7×D127
FittingC2×C7×C9×C127C2
socle, prime radicalC2×C3×C7×C127C2×C3
cosocleC2×C3×C127C2×C3×C7
LCSG ▷ C127
UCSC1 ◁ C2×C7×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32004

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 8);