Finite Group Databasebeta

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C2×#72221696 #72221697

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

Aliases

direct productC2×#72221696

Splittings

SylowC52 ⋊ C2×C4×#100

Subgroups

subgroupG/H
centerC22#13107468
commutatorC22×C52C22×C42
FrattiniC22C22×AGL(1,𝔽5)2
FittingC24×C52C42
socleC22×C52C4×C22⋊C4
prime radicalC22×#87886C22
cosocleC2×#6036C24
hypercenterC24AGL(1,𝔽5)2
hypocenterC52C2×C4×#100
LCSG ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C23 ◁ C24

4621 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221742
maximal normal subgroup of#72221742

GAP

Past the SmallGroups library coverage — no SmallGroups id.