Finite Group Databasebeta

#25003522

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC43×C22⋊#95 ⋊ C2
SylowC43 ⋊ #11043

Subgroups

subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC43×C22⋊#95C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#11043
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=g,b^2=d,b^a=bd,c^a=ce,e^a=eh,i^a=i^42,c^b=cf,g^c=gh,i^c=i^42

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 76493);