Finite Group Databasebeta

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C7×Dic5×C73⋊C3 #44501270

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic5×C73⋊C3
unambiguous semidirect product(Dic5×C73)⋊(C3×C7)

Splittings

derived, HallC5×C73 ⋊ C3×C4×C7
HallC7×Dic5×C73 ⋊ C3
HallC5×C7×C73⋊C3 ⋊ C4
HallC5×C7×C73 ⋊ C3×C4
HallDic5×C73 ⋊ C3×C7
HallC5×C73⋊C3 ⋊ C4×C7
HallC7×C73 ⋊ C3×Dic5
SylowC73 ⋊ C3×C7×Dic5
HallC5×C7 ⋊ C4×C73⋊C3
SylowC5 ⋊ C4×C7×C73⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7D5×C73⋊C3
commutator, hypocenterC5×C73C3×C4×C7
FrattiniC2C7×D5×C73⋊C3
Fitting, socleC2×C5×C7×C73C2×C3
prime radicalC2×C5×C7×C73⋊C3C2
cosocleC2×C5×C73C2×C3×C7
LCSG ▷ C5×C73
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 33);