Finite Group Databasebeta

#25001823

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC2×C43×#336 ⋊ C2
SylowC43 ⋊ #10715

Subgroups

subgroupG/H
center, FrattiniC23×C4C22×D43
commutatorC23×C43C2×C42
FittingC2×C43×#336C2
socleC24×C43C22×C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#336D43
hypocenterC43#10715
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×#336

1534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,c^b=ch,i^c=i^42

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, 74794);