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C2×C5×#11924781 #26046151

order11970
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#11924781

Splittings

Fitting, socle, HallC2×C5×C7×C19 ⋊ C9
derived, HallC7×C19 ⋊ C2×C5×C9
HallC5×C7×C19 ⋊ C2×C9
HallC2×C7×C19 ⋊ C5×C9
HallC2×C5×C19 ⋊ C7⋊C9
HallC5×C19 ⋊ C2×C7⋊C9
HallC2×C5×C7 ⋊ #4296
HallC2×C19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C2×#4296
SylowC19 ⋊ C2×C5×C7⋊C9
HallC2×C7 ⋊ C5×#4296
SylowC7 ⋊ C2×C5×#4296

Subgroups

subgroupG/H
center, hypercenterC2×C5#11924781
commutator, hypocenterC7×C19C2×C5×C9
FrattiniC1G
Fitting, socleC2×C5×C7×C19C9
prime radicalC2×C5×C7×C19⋊C3C3
cosocleC7×C19⋊C3C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

290 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#18012152, C5×#18012154, C5×#18012158, …
maximal normal subgroup ofC5×#18012152, C5×#18012154, C5×#18012158, …
maximal quotient ofC4×C5×#11924781, C22×C5×#11924781

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 80);