Finite Group Databasebeta

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C2×C4×#13093948 #26214022

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#13093948

Splittings

SylowC47 ⋊ C2×C4×#103

Subgroups

subgroupG/H
centerC23×C4C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×C4×Q8×C47C2
socle, prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC22×C4×Q8D47
hypocenterC47C2×C4×#103
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×Q8

1726 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167312);