Finite Group Databasebeta

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Q16×C22⋊Dic43 #25112459

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ16×C22⋊Dic43

Splittings

SylowC43 ⋊ C22⋊C4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC23×Q16×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC23×Q16D43
hypocenterC43C22⋊C4×Q16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

1398 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 185430);