Finite Group Databasebeta

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C2×C3×#11924174 #72246483

order7056
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3×#11924174

Splittings

derived, SylowC72 ⋊ C22×C32×C4
HallC2×#87639 ⋊ C32
HallC3×#3861 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22×C3#64423⋊C2
commutator, hypocenterC72C22×C32×C4
FrattiniC2C2×C3×#64423⋊C2
Fitting, socleC22×C3×C72C22×C3
prime radicalC22×C3×#64424C2
cosocleC2×C72C23×C32
LCSG ▷ C72
UCSC1 ◁ C22×C3

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#11924174, C2×C3×#72210376, C2×#72222115
maximal normal subgroup ofC2×D3×#11924174, C2×C3×#72210376, C2×#72222115

GAP

Past the SmallGroups library coverage — no SmallGroups id.