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C5×#14558781 #26046095

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

Aliases

direct productC5×#14558781

Splittings

derived, HallC7×C19 ⋊ C2×C5×C9
HallC5×#11924777 ⋊ C2
HallC5×C7×D19 ⋊ C9
Hall#11924777 ⋊ C2×C5
HallC5×C7×C19 ⋊ C2×C9
HallC7×D19 ⋊ C5×C9
HallC5×D19 ⋊ C7⋊C9
HallC5×C19 ⋊ C2×C7⋊C9
HallD19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ #4294⋊C2
SylowC19 ⋊ C2×C5×C7⋊C9
SylowC7 ⋊ C5×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C5#11716322
commutator, hypocenterC7×C19C2×C5×C9
FrattiniC3C5×#11716322
Fitting, socleC3×C5×C7×C19C2×C3
prime radicalC3×C5×C7×D19C3
cosocleC3×C7×C19C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

465 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#14558781⋊C2, #14558781⋊D5, D5×#14558781, …
maximal normal subgroup ofC5×#14558781⋊C2, #14558781⋊D5, D5×#14558781, …
maximal quotient ofC5×#18012091, C2×C5×#14558781

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 24);