Finite Group Databasebeta

← Prev (#38760292) Next (#38760294) →

C7×C3⋊(Dic43⋊C7) #38760293

order25284
automorphism?
homologyAbelianization (H1) = C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC7×C3⋊(Dic43⋊C7)
unambiguous semidirect productC3⋊(C7×Dic43⋊C7)
unambiguous semidirect product(C43⋊C7)⋊(C7×Dic3)
unambiguous semidirect productDic129⋊C72
unambiguous semidirect product(C7×Dic129)⋊C7

Splittings

derived, HallC3×C43 ⋊ C4×C72
HallC3×C7×C43⋊C7 ⋊ C4
HallC7×C43⋊C7 ⋊ Dic3
HallDic129 ⋊ C72
SylowC43 ⋊ C72×Dic3
SylowC3 ⋊ C7×Dic43⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(D43⋊C7)
commutator, hypocenterC3×C43C4×C72
FrattiniC2C7×C3⋊(D43⋊C7)
Fitting, socleC2×C3×C7×C43C2×C7
prime radicalC2×C3×C7×C43⋊C7C2
cosocleC2×C3×C43C2×C72
LCSG ▷ C3×C43
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3612

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 100);