Finite Group Databasebeta

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C2×C5×#14555735 #36372575

order22230
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#14555735

Splittings

derived, HallC13×C19 ⋊ C2×C5×C9
HallC2×C5×C13×C19 ⋊ C9
HallC5×C13×C19 ⋊ C2×C9
HallC2×C13×C19 ⋊ C5×C9
HallC2×C5×C19 ⋊ C13⋊C9
HallC2×C5×C13 ⋊ #4294
HallC5×C19 ⋊ C2×C13⋊C9
HallC5×C13 ⋊ C2×#4294
HallC2×C19 ⋊ C5×C13⋊C9
HallC2×C13 ⋊ C5×#4294
SylowC19 ⋊ C2×C5×C13⋊C9
SylowC13 ⋊ C2×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5#10625202
commutator, hypocenterC13×C19C2×C5×C9
FrattiniC3C2×C5×#10625202
Fitting, socle, prime radicalC2×C3×C5×C13×C19C3
cosocleC3×C13×C19C2×C3×C5
LCSG ▷ C13×C19
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22230

Conjugacy classes & character table

2550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22230, 4);