Finite Group Databasebeta

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C2×#72236796 #72344177

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#72236796

Subgroups

subgroupG/H
centerC2×C4C2×#1020⋊C2
commutator, hypocenter#997C23×C4
FrattiniC22×C4C23×S4
FittingC22×#3025D3
socleC22C2×#73080
prime radicalC22×#3025⋊C3C2
cosocle#5950C24
hypercenterC22×C4#1020⋊C2
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C22×C4

9058 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 64

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72240979, C2×#72236967, C2×#72240984
maximal normal subgroup ofC2×#72240979, C2×#72236967, C2×#72240984

GAP

Past the SmallGroups library coverage — no SmallGroups id.