Finite Group Databasebeta

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C2×C4×#1842⋊C3 #72212885

order3072
isoclinismisoclinic class of #127⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C42

Aliases

direct productC2×C4×#1842⋊C3

Splittings

Fitting, SylowC2×C4×#1842 ⋊ C3
derivedC42 ⋊ C2×C3×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C42#127⋊C3
commutator, hypocenterC42C2×C3×C4×C8
FrattiniC23×C4C23×A4
FittingC2×C4×#1842C3
socleC25C2×C4×A4
prime radicalC23×C42⋊C3C2×C4
cosocleC2×C43C23×C3
LCSG ▷ C42
UCSC1 ◁ C2×C42

4796 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#72211696, #72218219
maximal normal subgroup of#72218219

GAP

Past the SmallGroups library coverage — no SmallGroups id.