Finite Group Databasebeta

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C4⋊C8×Dic94 #26235071

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C8×Dic94

Splittings

SylowC47 ⋊ Q8×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC4×C4⋊C8×C47C2
socle, prime radicalC23×C47C23×C4
cosocleC22×C4×C47C24
hypercenterC4×C4⋊C8D47
hypocenterC47Q8×C4⋊C8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C8

896 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, 188361);