Finite Group Databasebeta

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C2×#72227572 #72267945

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

Aliases

direct productC2×#72227572

Subgroups

subgroupG/H
centerC22×C4C2×#1020
commutatorC2×C22⋊SL(2,𝔽3)C22×C4
FrattiniC2×C4C22×#1020
FittingC25×#41D3
socleC25C2×SL(2,ℤ/4)
prime radicalC23×#5948C2
cosocleC2×#5948C23
hypercenterC23×C4#1020
hypocenterC22⋊SL(2,𝔽3)C2×C22⋊C4
LCSG ▷ C2×C22⋊SL(2,𝔽3) ▷ C22⋊SL(2,𝔽3)
UCSC1 ◁ C22×C4 ◁ C23×C4

At least 8601 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72267959
maximal normal subgroup of#72267959

GAP

Past the SmallGroups library coverage — no SmallGroups id.