Finite Group Databasebeta

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C23×#13063351 #26010389

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×#13063351

Splittings

FittingC24×D4×C43 ⋊ C2
SylowC43 ⋊ C23×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC24×D4×C43C2
socleC24×C43C2×D4
hypercenterC24×D4D43
hypocenterC43C23×AGL(1,ℤ/8)
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C24×D4

13310 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083360);