Finite Group Databasebeta

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Q16×Dic47⋊C4 #26234705

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ16×Dic47⋊C4

Splittings

SylowC47 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×Q16×C47C2
socle, prime radicalC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×C4×Q16D47
hypocenterC47C4⋊C4×Q16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

926 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 187995);