Finite Group Databasebeta

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C2×#13101682 #72221070

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

Aliases

direct productC2×#13101682

Splittings

SylowC52 ⋊ C22×#100

Subgroups

subgroupG/H
centerC22#11717092
commutatorC22×C52C23×C4
FrattiniC2×C4C22×D52
FittingC22×C52×D4C22
socleC22×C52C2×C22⋊C4
prime radicalC22×D4×C5⋊D5C2
cosocleC2×C4×C52C24
hypercenterC22×D4D52
hypocenterC52C22×#100
LCSG ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

3346 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72213351, #72223210, C2×#72213490, …
maximal normal subgroup ofC2×#72213351, #72223210, C2×#72213490, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.