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C7×Dic1335 #49153121

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

Aliases

direct productC7×Dic1335
unambiguous semidirect productC3⋊(C7×Dic445)

Splittings

derived, HallC3×C5×C89 ⋊ C4×C7
HallC3×C5×C7×C89 ⋊ C4
HallC5×C7×C89 ⋊ Dic3
HallC3×C7×C89 ⋊ Dic5
HallC7×C89 ⋊ Dic15
HallC5×C89 ⋊ C7×Dic3
HallC3×C89 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ Dic89
SylowC89 ⋊ C7×Dic15
HallC5×C7 ⋊ Dic267
HallC3×C7 ⋊ Dic445
HallC3×C5 ⋊ C7×Dic89
SylowC5 ⋊ C7×Dic267
SylowC3 ⋊ C7×Dic445

Subgroups

subgroupG/H
center, hypercenterC2×C7D1335
commutator, hypocenterC3×C5×C89C4×C7
FrattiniC2C7×D1335
Fitting, socle, prime radicalC2×C3×C5×C7×C89C2
cosocleC2×C3×C5×C89C2×C7
LCSG ▷ C3×C5×C89
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37380

Conjugacy classes & character table

9366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 15);