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C5×#14558808 #26046129

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

Aliases

direct productC5×#14558808

Splittings

Fitting, socle, HallC5×C7×C19 ⋊ C2×C9
derived, HallC7×C19 ⋊ C2×C5×C9
HallC5×#11924781 ⋊ C2
HallC5×C7×D19 ⋊ C9
Hall#11924781 ⋊ C2×C5
HallC7×D19 ⋊ C5×C9
HallC5×D19 ⋊ C7⋊C9
HallC5×C19 ⋊ C2×C7⋊C9
HallD19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ AGL(1,𝔽19)
SylowC19 ⋊ C2×C5×C7⋊C9
SylowC7 ⋊ C5×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC5#14558808
commutator, hypocenterC7×C19C2×C5×C9
FrattiniC1G
Fitting, socleC5×C7×C19C2×C9
prime radicalC5×C7×D19⋊C3C3
cosocleC7×C19⋊C3C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

185 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#14558802⋊C2, #14558808⋊D5, D5×#14558808, …
maximal normal subgroup ofC5×#14558802⋊C2, #14558808⋊D5, D5×#14558808, …
maximal quotient ofC5×#18012158, C2×C5×#14558808

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 58);