Finite Group Databasebeta

← Prev (#44447126) Next (#44447128) →

C5×C7×Dic213 #44447127

order29820
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic213
unambiguous semidirect productC3⋊(C5×C7×Dic71)

Splittings

derived, HallC3×C71 ⋊ C4×C5×C7
HallC3×C5×C7×C71 ⋊ C4
HallC5×C7×C71 ⋊ Dic3
HallC3×C7×C71 ⋊ C4×C5
HallC3×C5×C71 ⋊ C4×C7
HallC7×C71 ⋊ C5×Dic3
HallC5×C71 ⋊ C7×Dic3
HallC3×C5×C7 ⋊ Dic71
SylowC71 ⋊ C5×C7×Dic3
HallC3×C7 ⋊ C5×Dic71
HallC3×C5 ⋊ C7×Dic71
SylowC3 ⋊ C5×C7×Dic71

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D213
commutator, hypocenterC3×C71C4×C5×C7
FrattiniC2C5×C7×D213
Fitting, socle, prime radicalC2×C3×C5×C7×C71C2
cosocleC2×C3×C71C2×C5×C7
LCSG ▷ C3×C71
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29820

Conjugacy classes & character table

7560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 15);