Finite Group Databasebeta

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C4×#72209772 #72247140

order6144
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#72209772

Splittings

FittingC4×#62817 ⋊ D3
derived#11710730 ⋊ C2×C4

Subgroups

subgroupG/H
centerC2×C4#11715850
commutator, hypocenter#11710730C2×C4
FrattiniC23C2×#87588
FittingC4×#62817D3
socleC22C2×#11715850
prime radicalC2×#72209772C2
cosocleC2×#11710730C22
hypercenterC22×C4#87588
LCSG ▷ #11710730
UCSC1 ◁ C2×C4 ◁ C22×C4

At least 10192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has at least 10192 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#72209832, C4×#72215868
maximal normal subgroup ofC4×#72209832

GAP

Past the SmallGroups library coverage — no SmallGroups id.