Finite Group Databasebeta

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D5×#12707 #72242979

order2560
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD5×#12707

Splittings

FittingC5×#12707 ⋊ C2
SylowC5 ⋊ C2×#12707

Subgroups

subgroupG/H
centerC2D5×#1781
commutatorC22×C4×C5C23×C4
FrattiniC22×D4C23×D5
FittingC5×#12707C2
socleC2×C5C2×#1781
prime radicalD5×#3484C2
cosocleC22×C5×D4C24
hypercenter#12707D5
hypocenterC5C2×#12707
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C23 ◁ C23×D4 ◁ #12707

8536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72242993, AGL(1,𝔽5)×#12707, D5×#511790
maximal normal subgroup of#72242993, AGL(1,𝔽5)×#12707, D5×#511790

GAP

Past the SmallGroups library coverage — no SmallGroups id.