Finite Group Databasebeta

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C4×#11714174 #72341370

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

Aliases

direct productC4×#11714174

Splittings

FittingC4×#3027 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C2×#1020⋊C2
commutator, hypocenter#997C23×C4
FrattiniC24C23×S4
FittingC4×#3027D3
socleC22C22×#1020⋊C2
prime radicalC2×#11714174C2
cosocleC2×#997C24
hypercenterC42#1020⋊C2
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C42

7210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 64

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#72217027, #72342093
maximal normal subgroup ofC4×#72217027, #72342093

GAP

Past the SmallGroups library coverage — no SmallGroups id.