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C5×Dic9×C107 #34064074

order19260
automorphism?
homologyAbelianization (H1) = C4×C5×C107 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic9×C107
unambiguous semidirect productC9⋊(C4×C5×C107)

Splittings

derived, SylowC9 ⋊ C4×C5×C107
HallC5×C9×C107 ⋊ C4
HallC9×C107 ⋊ C4×C5
HallC5×C9 ⋊ C4×C107

Subgroups

subgroupG/H
center, hypercenterC2×C5×C107D9
commutator, hypocenterC9C4×C5×C107
FrattiniC2×C3C5×D3×C107
FittingC2×C5×C9×C107C2
socle, prime radicalC2×C3×C5×C107D3
cosocleC2×C9C2×C5×C107
LCSG ▷ C9
UCSC1 ◁ C2×C5×C107

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19260

Conjugacy classes & character table

6420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19260, 5);