Finite Group Databasebeta

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D5×D5⋊#100 #72221627

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD5×D5⋊#100

Splittings

SylowC52 ⋊ C22×#100

Subgroups

subgroupG/H
centerC2C2×D5×C22⋊AGL(1,𝔽5)
commutatorC22×C52C23×C4
FrattiniC22C22×D5×AGL(1,𝔽5)
FittingC2×C52×D4C2×C4
socleC2×C52C22×C22⋊C4
prime radicalC2×D4×D52C2
cosocleC2×C5×Dic5C24
hypercenterC2×D4D5×AGL(1,𝔽5)
hypocenterC52C22×#100
LCSG ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

2102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221763, #72221764, #72221767, …
maximal normal subgroup of#72221763, #72221764, #72221767, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.