Finite Group Databasebeta

← Prev (#25266942) Next (#25266944) →

#25266943

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

No aliases for this group.

Splittings

FittingC2×C4×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ #34840

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C4×C4⋊C4×C43C2
prime radicalC22×C22⋊D43C23
hypercenterC2×C4×C4⋊C4D43
hypocenterC43#34840
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

1944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=g,c^2=gh,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,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, 339914);