Finite Group Databasebeta

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C3×C7×Dic377 #44539715

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic377

Splittings

derived, HallC13×C29 ⋊ C3×C4×C7
HallC3×C7×C13×C29 ⋊ C4
HallC7×C13×C29 ⋊ C3×C4
HallC3×C13×C29 ⋊ C4×C7
HallC3×C7×C29 ⋊ Dic13
HallC3×C7×C13 ⋊ Dic29
HallC7×C29 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic29
HallC3×C29 ⋊ C7×Dic13
HallC3×C13 ⋊ C7×Dic29
SylowC29 ⋊ C3×C7×Dic13
SylowC13 ⋊ C3×C7×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D377
commutator, hypocenterC13×C29C3×C4×C7
FrattiniC2C3×C7×D377
Fitting, socle, prime radicalC2×C3×C7×C13×C29C2
cosocleC2×C13×C29C2×C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31668

Conjugacy classes & character table

7980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 10);