Finite Group Databasebeta

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C4×#15689539 #26368920

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#15689539

Splittings

FittingC2×C4×C16×C47 ⋊ C2
SylowC47 ⋊ C4×#504

Subgroups

subgroupG/H
centerC4×C16C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC2×C8C23×D47
FittingC2×C4×C16×C47C2
socleC22×C47C23×C8
prime radicalC2×#10625350C2×C4
cosocleC2×C8×C47C24
hypercenterC2×C4×C16D47
hypocenterC47C4×#504
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

834 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322210);