Finite Group Databasebeta

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C4×Q8×C22⋊D47 #26376140

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×Q8×C22⋊D47

Splittings

FittingC22×C4×Q8×C47 ⋊ C2
SylowC47 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×C4×Q8×C47C2
socle, cosocleC23×C47C25
prime radicalC22×C22⋊D47C23
hypercenterC22×C4×Q8D47
hypocenterC47C4×D4×Q8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

3148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 329430);