Finite Group Databasebeta

#24987401

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #8204

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C2×C42
FrattiniC2×C42C22×D43
FittingC2×C8×D4×C43C2
socleC23×C43C4×D4
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC2×C8×D4D43
hypocenterC43#8204
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×D4

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=e,b^2=f,c^2=e,d^2=g,e^2=h,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cgh,i^b=i^42

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60372);