Finite Group Databasebeta

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C5×Dic1071 #36339181

order21420
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1071
unambiguous semidirect productC7⋊(C5×Dic153)
unambiguous semidirect productC9⋊(C5×Dic119)

Splittings

derived, HallC7×C9×C17 ⋊ C4×C5
HallC5×C7×C9×C17 ⋊ C4
HallC5×C9×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ Dic9
HallC5×C7×C9 ⋊ Dic17
HallC9×C17 ⋊ C5×Dic7
HallC7×C17 ⋊ C5×Dic9
HallC5×C17 ⋊ Dic63
HallC7×C9 ⋊ C5×Dic17
HallC5×C9 ⋊ Dic119
HallC5×C7 ⋊ Dic153
SylowC17 ⋊ C5×Dic63
SylowC9 ⋊ C5×Dic119
SylowC7 ⋊ C5×Dic153

Subgroups

subgroupG/H
center, hypercenterC2×C5D1071
commutator, hypocenterC7×C9×C17C4×C5
FrattiniC2×C3C5×D357
FittingC2×C5×C7×C9×C17C2
socle, prime radicalC2×C3×C5×C7×C17D3
cosocleC2×C7×C9×C17C2×C5
LCSG ▷ C7×C9×C17
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

5370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 13);