Finite Group Databasebeta

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C5×#20259496 #44501288

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#20259496

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C3×C4
derived, HallC7×C73 ⋊ C3×C4×C5
HallC5×C7⋊#64408 ⋊ C3
HallC5×#13095275 ⋊ C4
HallC7⋊#64408 ⋊ C3×C5
Hall#13095275 ⋊ C4×C5
HallC5×C73 ⋊ ΓL(1,𝔽8)⋊C4
SylowC73 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ #64408⋊C3
SylowC7 ⋊ C5×#64408⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#20259496
commutator, hypocenterC7×C73C3×C4×C5
FrattiniC1G
Fitting, socleC5×C7×C73C3×C4
prime radicalC5×#15690441C2
cosocleC7×D73C2×C3×C5
LCSG ▷ C7×C73
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2555

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 51);