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C7×Dic1035 #44394346

order28980
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic1035
unambiguous semidirect productC9⋊(C7×Dic115)
unambiguous semidirect productC23⋊(C7×Dic45)

Splittings

derived, HallC5×C9×C23 ⋊ C4×C7
HallC5×C7×C9×C23 ⋊ C4
HallC7×C9×C23 ⋊ Dic5
HallC5×C7×C23 ⋊ Dic9
HallC5×C7×C9 ⋊ Dic23
HallC9×C23 ⋊ C7×Dic5
HallC7×C23 ⋊ Dic45
HallC5×C23 ⋊ C7×Dic9
HallC7×C9 ⋊ Dic115
HallC5×C9 ⋊ C7×Dic23
HallC5×C7 ⋊ Dic207
SylowC23 ⋊ C7×Dic45
SylowC9 ⋊ C7×Dic115
SylowC5 ⋊ C7×Dic207

Subgroups

subgroupG/H
center, hypercenterC2×C7D1035
commutator, hypocenterC5×C9×C23C4×C7
FrattiniC2×C3C7×D345
FittingC2×C5×C7×C9×C23C2
socle, prime radicalC2×C3×C5×C7×C23D3
cosocleC2×C5×C9×C23C2×C7
LCSG ▷ C5×C9×C23
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

7266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 15);