Finite Group Databasebeta

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C2×#72236845 #72343489

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#72236845

Splittings

FittingC2×#63076 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C22×#1020
commutator, hypocenter#997C23×C4
FrattiniC4C23×#1020
FittingC2×#63076D3
socleC22C2×C4×#1020
prime radicalC22×#87519C2
cosocle#5950C24
hypercenterC2×M16#1020
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C2×M16

24371 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 64

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72240989, C2×#72240994, C2×#72236967
maximal normal subgroup ofC2×#72240989, C2×#72240994, C2×#72236967

GAP

Past the SmallGroups library coverage — no SmallGroups id.