Finite Group Databasebeta

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C5×C4⋊#157 #10624102

order720
isoclinismisoclinic class of #3788
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×C4⋊#157
unambiguous semidirect productC4⋊(C5×#157)

Splittings

FittingC32×C4×C5 ⋊ C4
HallC32×C5 ⋊ C4⋊C4
SylowC32 ⋊ C5×C4⋊C4

Subgroups

subgroupG/H
centerC2×C5C2×#157
commutatorC2×C32C2×C4×C5
FrattiniC2C2×C5×#157
FittingC32×C4×C5C4
socleC2×C32×C5C2×C4
prime radicalC2×C5×C3⋊D3C22
cosocleC2×C3⋊D3C22×C5
hypercenterC4×C5#157
hypocenterC32C5×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13085502, #13085504, #13085510, …
maximal normal subgroup of#13085502, #13085504, #13085510, …
maximal quotient ofC5×#63768, C5×#63769, C5×#63770, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 571);