Finite Group Databasebeta

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C2×#72227646 #72271668

order3072
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#72227646

Subgroups

subgroupG/H
centerC2×C4#87524
commutator#5950C22×C4
FrattiniC2×C4C22×#1020
FittingC2×#63103D3
socleC22#11715569
prime radicalC2×#11710937C2
cosocleC2×#5950C23
hypercenterC2×#41#1020
hypocenter#997C2×C22⋊C4
LCSG ▷ #5950 ▷ #997
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Only the 176 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72271725
maximal normal subgroup of#72271725

GAP

Past the SmallGroups library coverage — no SmallGroups id.