Finite Group Databasebeta

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C127×Dic63 #44544631

order32004
automorphism?
homologyAbelianization (H1) = C4×C127 · Schur multiplier (H2) = C1

Aliases

direct productC127×Dic63
unambiguous semidirect productC7⋊(Dic9×C127)
unambiguous semidirect productC9⋊(Dic7×C127)

Splittings

derived, HallC7×C9 ⋊ C4×C127
HallC7×C9×C127 ⋊ C4
HallC9×C127 ⋊ Dic7
HallC7×C127 ⋊ Dic9
SylowC9 ⋊ Dic7×C127
SylowC7 ⋊ Dic9×C127

Subgroups

subgroupG/H
center, hypercenterC2×C127D63
commutator, hypocenterC7×C9C4×C127
FrattiniC2×C3D21×C127
FittingC2×C7×C9×C127C2
socle, prime radicalC2×C3×C7×C127D3
cosocleC2×C7×C9C2×C127
LCSG ▷ C7×C9
UCSC1 ◁ C2×C127

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32004

Conjugacy classes & character table

8382 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 13);