Finite Group Databasebeta

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C3×C7×Dic3×C127 #44544766

order32004
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C127 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic3×C127
unambiguous semidirect productC3⋊(C3×C4×C7×C127)

Splittings

derivedC3 ⋊ C3×C4×C7×C127
HallC32×C7×C127 ⋊ C4
HallC32×C127 ⋊ C4×C7
HallC32×C7 ⋊ C4×C127
SylowC32 ⋊ C4×C7×C127

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C127D3
commutator, hypocenterC3C3×C4×C7×C127
FrattiniC2C3×D3×C7×C127
Fitting, socle, prime radicalC2×C32×C7×C127C2
cosocleC2×C3C2×C3×C7×C127
LCSG ▷ C3
UCSC1 ◁ C2×C3×C7×C127

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10668

Conjugacy classes & character table

16002 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 148);