Finite Group Databasebeta

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Q8⋊C8×Dic47 #26106877

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productQ8⋊C8×Dic47

Splittings

SylowC47 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47C4×Q8⋊C8
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

654 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, 60167);