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C7×Dic645 #31825344

order18060
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic645
unambiguous semidirect productC3⋊(C7×Dic215)

Splittings

derived, HallC3×C5×C43 ⋊ C4×C7
HallC3×C5×C7×C43 ⋊ C4
HallC5×C7×C43 ⋊ Dic3
HallC3×C7×C43 ⋊ Dic5
HallC7×C43 ⋊ Dic15
HallC5×C43 ⋊ C7×Dic3
HallC3×C43 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ Dic43
SylowC43 ⋊ C7×Dic15
HallC5×C7 ⋊ Dic129
HallC3×C7 ⋊ Dic215
HallC3×C5 ⋊ C7×Dic43
SylowC5 ⋊ C7×Dic129
SylowC3 ⋊ C7×Dic215

Subgroups

subgroupG/H
center, hypercenterC2×C7D645
commutator, hypocenterC3×C5×C43C4×C7
FrattiniC2C7×D645
Fitting, socle, prime radicalC2×C3×C5×C7×C43C2
cosocleC2×C3×C5×C43C2×C7
LCSG ▷ C3×C5×C43
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18060

Conjugacy classes & character table

4536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 20);