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C5×#14268588 #22583299

order9030
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#14268588

Splittings

Fitting, socle, HallC5×C7×C43 ⋊ C2×C3
derived, HallC7×C43 ⋊ C2×C3×C5
HallC5×#11744749 ⋊ C2
HallC5×C7×D43 ⋊ C3
Hall#11744749 ⋊ C2×C5
HallC7×D43 ⋊ C3×C5
HallC5×D43 ⋊ ΓL(1,𝔽8)
HallC5×C43 ⋊ C2×ΓL(1,𝔽8)
HallD43 ⋊ C5×ΓL(1,𝔽8)
SylowC43 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ D43⋊C3
SylowC7 ⋊ C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#14268588
commutator, hypocenterC7×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

295 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#14268588⋊C2, #14268588⋊D5, D5×#14268588, …
maximal normal subgroup ofC5×#14268588⋊C2, #14268588⋊D5, D5×#14268588, …
maximal quotient ofC5×#16813401, C2×C5×#14268588, C5×#19129334, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 32);