Finite Group Databasebeta

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C22⋊Q8×C47⋊C8 #26223693

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

Aliases

direct productC22⋊Q8×C47⋊C8

Splittings

SylowC47 ⋊ C8×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC4×C22⋊Q8×C47C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC4×C22⋊Q8D47
hypocenterC47C8×C22⋊Q8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

990 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 176983);