Finite Group Databasebeta

← Prev (#44447129) Next (#44447131) →

C7×Dic15×C71 #44447130

order29820
automorphism?
homologyAbelianization (H1) = C4×C7×C71 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic15×C71
unambiguous semidirect productC3⋊(C7×Dic5×C71)

Splittings

derived, HallC3×C5 ⋊ C4×C7×C71
HallC3×C5×C7×C71 ⋊ C4
HallC5×C7×C71 ⋊ Dic3
HallC3×C7×C71 ⋊ Dic5
HallC3×C5×C71 ⋊ C4×C7
HallC5×C71 ⋊ C7×Dic3
HallC3×C71 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ C4×C71
HallC5×C7 ⋊ Dic3×C71
HallC3×C7 ⋊ Dic5×C71
SylowC5 ⋊ C7×Dic3×C71
SylowC3 ⋊ C7×Dic5×C71

Subgroups

subgroupG/H
center, hypercenterC2×C7×C71D15
commutator, hypocenterC3×C5C4×C7×C71
FrattiniC2C7×D15×C71
Fitting, socle, prime radicalC2×C3×C5×C7×C71C2
cosocleC2×C3×C5C2×C7×C71
LCSG ▷ C3×C5
UCSC1 ◁ C2×C7×C71

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29820

Conjugacy classes & character table

8946 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 18);