Finite Group Databasebeta

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C4×#15688869 #26107226

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#15688869

Splittings

SylowC47 ⋊ C4×#332

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC4×C4⋊Q8×C47C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×C4⋊Q8D47
hypocenterC47C4×#332
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊Q8

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60516);