Finite Group Databasebeta

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C22×#15688899 #26368904

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#15688899

Splittings

SylowC47 ⋊ C22×#346

Subgroups

subgroupG/H
centerC23×C8C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC2×C8C23×D47
FittingC22×C4×C8×C47C2
socle, prime radicalC24×C47C2×C8
cosocleC2×C8×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C22×#346
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

942 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, 322194);