Finite Group Databasebeta

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C7×Dic765 #36339183

order21420
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic765
unambiguous semidirect productC9⋊(C7×Dic85)

Splittings

derived, HallC5×C9×C17 ⋊ C4×C7
HallC5×C7×C9×C17 ⋊ C4
HallC7×C9×C17 ⋊ Dic5
HallC5×C7×C17 ⋊ Dic9
HallC5×C7×C9 ⋊ Dic17
HallC9×C17 ⋊ C7×Dic5
HallC7×C17 ⋊ Dic45
HallC5×C17 ⋊ C7×Dic9
HallC7×C9 ⋊ Dic85
HallC5×C9 ⋊ C7×Dic17
HallC5×C7 ⋊ Dic153
SylowC17 ⋊ C7×Dic45
SylowC9 ⋊ C7×Dic85
SylowC5 ⋊ C7×Dic153

Subgroups

subgroupG/H
center, hypercenterC2×C7D765
commutator, hypocenterC5×C9×C17C4×C7
FrattiniC2×C3C7×D255
FittingC2×C5×C7×C9×C17C2
socle, prime radicalC2×C3×C5×C7×C17D3
cosocleC2×C5×C9×C17C2×C7
LCSG ▷ C5×C9×C17
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

5376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 15);