Finite Group Databasebeta

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C7×Dic139⋊C9 #46855977

order35028
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic139⋊C9
unambiguous semidirect productDic139⋊(C7×C9)
unambiguous semidirect product(C139⋊C9)⋊(C4×C7)

Splittings

derived, SylowC139 ⋊ C4×C7×C9
HallC7×C139⋊C9 ⋊ C4
HallC7×Dic139 ⋊ C9
HallC139⋊C9 ⋊ C4×C7
HallC7×C139 ⋊ C4×C9
HallDic139 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D139⋊C3
commutator, hypocenterC139C4×C7×C9
FrattiniC2×C3C7×D139⋊C3
Fitting, socle, prime radicalC2×C3×C7×C139C2×C3
cosocleC2×C3×C139C2×C3×C7
LCSG ▷ C139
UCSC1 ◁ C2×C3×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35028

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 13);