Finite Group Databasebeta

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C2×#72236849 #72343200

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

Aliases

direct productC2×#72236849

Splittings

FittingC2×#21483 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C2×#1020⋊C2
commutator, hypocenter#997C23×C4
FrattiniC22×C4C23×S4
FittingC2×#21483D3
socleC22C4×#1020⋊C2
prime radicalC2×#11714162C2
cosocle#5950C24
hypercenterC2×C8#1020⋊C2
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C2×C8

6155 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×#72240992, C2×#72240996, C2×#72236967
maximal normal subgroup ofC2×#72240992, C2×#72240996, C2×#72236967

GAP

Past the SmallGroups library coverage — no SmallGroups id.