Finite Group Databasebeta

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C8×#13094015 #26224579

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productC8×#13094015

Splittings

SylowC47 ⋊ C8×#125

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC8×C4⋊C4×C47C2
socle, prime radicalC23×C47C23×C4
cosocleC22×C4×C47C24
hypercenterC8×C4⋊C4D47
hypocenterC47C8×#125
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

742 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 177869);