Finite Group Databasebeta

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#106×D5⋊AGL(1,𝔽5) #72242524

order6400
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct product#106×D5⋊AGL(1,𝔽5)

Splittings

FittingC52×#106 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#106

Subgroups

subgroupG/H
centerC22D4×D5⋊AGL(1,𝔽5)
commutatorC4×C52C22×C42
FrattiniC2×C4C22×D5⋊AGL(1,𝔽5)
FittingC52×#106C2×C4
socleC22×C52C2×C4×D4
prime radicalC22×D52C2×D4
cosocleC2×C4×C5⋊D5C24
hypercenter#106D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#106
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

2996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72269234
maximal normal subgroup of#72269234

GAP

Past the SmallGroups library coverage — no SmallGroups id.