Finite Group Databasebeta

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C4×#15688878 #26121425

order12032
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#15688878

Splittings

SylowC47 ⋊ C4×#336

Subgroups

subgroupG/H
centerC22×C42C2×D47
commutatorC2×C47C42×C8
FrattiniC23×C4C22×D47
FittingC2×C43×C47C2
socle, prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC2×C43D47
hypocenterC47C4×#336
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C42 ◁ C2×C43

1318 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, 74715);