Finite Group Databasebeta

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C3×C7×Dic43⋊C7 #38760290

order25284
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C7×Dic43⋊C7
unambiguous semidirect product(C3×Dic43)⋊C72
unambiguous semidirect product(C3×C7×Dic43)⋊C7

Splittings

derived, SylowC43 ⋊ C3×C4×C72
HallC3×C7×C43⋊C7 ⋊ C4
HallC7×C43⋊C7 ⋊ C3×C4
HallC3×Dic43 ⋊ C72
HallDic43 ⋊ C3×C72
HallC3×C43 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D43⋊C7
commutator, hypocenterC43C3×C4×C72
FrattiniC2C3×C7×D43⋊C7
Fitting, socleC2×C3×C7×C43C2×C7
prime radicalC2×C3×C7×C43⋊C7C2
cosocleC2×C43C2×C3×C72
LCSG ▷ C43
UCSC1 ◁ C2×C3×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3612

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 97);