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C5×#15690441 #29506455

order15330
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#15690441

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C2×C3
derived, HallC7×C73 ⋊ C2×C3×C5
HallC5×#13095275 ⋊ C2
HallC5×C7×D73 ⋊ C3
Hall#13095275 ⋊ C2×C5
HallC7×D73 ⋊ C3×C5
HallC5×D73 ⋊ ΓL(1,𝔽8)
HallC5×C73 ⋊ C2×ΓL(1,𝔽8)
HallD73 ⋊ C5×ΓL(1,𝔽8)
SylowC73 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ D73⋊C3
SylowC7 ⋊ C5×D73⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#15690441
commutator, cosocle, hypocenterC7×C73C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C73C2×C3
LCSG ▷ C7×C73
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2555

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#20259496, C5×#15690441⋊C2, C5×#20259502, …
maximal normal subgroup ofC5×#20259496, C5×#15690441⋊C2, C5×#20259502, …
maximal quotient ofC5×#20259484, C2×C5×#15690441

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15330, 23);