Finite Group Databasebeta

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C5×C7×Dic3×C89 #49153116

order37380
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C89 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic3×C89
unambiguous semidirect productC3⋊(C4×C5×C7×C89)

Splittings

derived, SylowC3 ⋊ C4×C5×C7×C89
HallC3×C5×C7×C89 ⋊ C4
HallC3×C7×C89 ⋊ C4×C5
HallC3×C5×C89 ⋊ C4×C7
HallC3×C89 ⋊ C4×C5×C7
HallC3×C5×C7 ⋊ C4×C89
HallC3×C7 ⋊ C4×C5×C89
HallC3×C5 ⋊ C4×C7×C89

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C89D3
commutator, hypocenterC3C4×C5×C7×C89
FrattiniC2C5×D3×C7×C89
Fitting, socle, prime radicalC2×C3×C5×C7×C89C2
cosocleC2×C3C2×C5×C7×C89
LCSG ▷ C3
UCSC1 ◁ C2×C5×C7×C89

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37380

Conjugacy classes & character table

18690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 10);