Finite Group Databasebeta

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C22×#15688871 #26184570

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

Aliases

direct productC22×#15688871

Splittings

SylowC47 ⋊ C22×#333

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC22×C4⋊C8×C47C2
socle, prime radicalC24×C47C22⋊C4
cosocleC42×C47C24
hypercenterC22×C4⋊C8D47
hypocenterC47C22×#333
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1334 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 137860);