Finite Group Databasebeta

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C4×#15689273 #26221856

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#15689273

Splittings

FittingC4×C22⋊Q8×C47 ⋊ C2
SylowC47 ⋊ C4×#450

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C22⋊Q8×C47C2
socleC23×C47C22×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenterC4×C22⋊Q8D47
hypocenterC47C4×#450
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

1880 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, 175146);