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C5×C7×Dic207 #44394342

order28980
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic207
unambiguous semidirect productC9⋊(C5×C7×Dic23)
unambiguous semidirect productC23⋊(C5×C7×Dic9)

Splittings

derived, HallC9×C23 ⋊ C4×C5×C7
HallC5×C7×C9×C23 ⋊ C4
HallC7×C9×C23 ⋊ C4×C5
HallC5×C9×C23 ⋊ C4×C7
HallC5×C7×C23 ⋊ Dic9
HallC5×C7×C9 ⋊ Dic23
HallC7×C23 ⋊ C5×Dic9
HallC5×C23 ⋊ C7×Dic9
HallC7×C9 ⋊ C5×Dic23
HallC5×C9 ⋊ C7×Dic23
SylowC23 ⋊ C5×C7×Dic9
SylowC9 ⋊ C5×C7×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D207
commutator, hypocenterC9×C23C4×C5×C7
FrattiniC2×C3C5×C7×D69
FittingC2×C5×C7×C9×C23C2
socle, prime radicalC2×C3×C5×C7×C23D3
cosocleC2×C9×C23C2×C5×C7
LCSG ▷ C9×C23
UCSC1 ◁ C2×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 11);